Question 1

Ex 3.1 Class 10 Maths Question 1.
Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be”. Isn’t this interesting? Represent this situation algebraically and graphically.

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
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  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 2

Ex 3.1 Class 10 Maths Question 2.
The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 3 more balls of the same kind for ₹1300. Represent this situation algebraically and geometrically.

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 3

Ex 3.1 Class 10 Maths Question 3.
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be ₹160.  After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹300. Represent the situation algebraically and geometrically.

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 4

Ex 3.2 Class 10 Maths Question 1.
 Form the pair of linear equations of the following problems and find their solutions graphically:
(i) 10 students of class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
(ii) 5 pencils and 7 pens together cost ₹50, whereas 7 pencils and 5 pens together cost ₹46. Find the cost of one pencil and that of one pen.

Accepted Answer

Worksheets for Class 10 Maths

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 5

Ex 3.2 Class 10 Maths Question 2.
On comparing the ratios $\frac { { a }_{ 1 } }{ { a }_{ 2 } }$, $\frac { { b }_{ 1 } }{ { b }_{ 2 } }$
and $\frac { { c }_{ 1 } }{ { c }_{ 2 } }$ , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:
(i) 5x – 4y + 8 = 0, 7x + 6y – 9 = 0
(ii) 9x + 3y + 12 = 0, 18x + 6y + 24 = 0
(iii) 6x – 3y + 10 = 0, 2x -y + 9 = 0

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 6

Ex 3.2 Class 10 Maths Question 4.
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically.
(i) x + y = 5, 2x + 2y = 10
(ii) x-y – 8, 3x – 3y = 16
(iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0
(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 7

Ex 3.2 Class 10 Maths Question 6.
Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 8

Ex 3.2 Class 10 Maths Question 7.
Draw the, graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 9

Ex 3.2 Class 10 Maths Question 3.
On comparing the ratios $\frac { { a }_{ 1 } }{ { a }_{ 2 } }$, $\frac { { b }_{ 1 } }{ { b }_{ 2 } }$
and $\frac { { c }_{ 1 } }{ { c }_{ 2 } }$, find out whether the following pairs of linear equations are consistent, or inconsistent:
~

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 10

Ex 3.2 Class 10 Maths Question 5.
Half the perimeter of a rectangular garden, whose length is 4 m more than its width is 36 m. Find the dimensions of the garden graphically.

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 11

Ex 3.3 Class 10 Maths Question 1.
Solve the following pairs of linear equations by the substitution method:

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 12

Ex 3.3 Class 10 Maths Question 3.
Form the pair of linear equations for the following problems and find their solution by substitution method:
(i) The difference between two numbers is 26 and one number is three times the other. Find them.
(ii) The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
(iii) The coach of a cricket team buys 7 bats and 6 balls for ₹3800. Later, she buys 3 bats and 5 balls for ₹1750. Find the cost of each bat and each ball.
(iv) The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹105 and for a journey of 15 km, the charge paid is ₹155. What are the fixed charges and the charges per km? How much does a person have to pay for travelling a distance of 25 km?
(v) A fraction becomes $\frac { 9 }{ 11 }$, if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes $\frac { 5 }{ 6 }$. Find the fraction.
(vi) Five years hence, the age of Jacob will be three times that of his son. Five year ago, Jacob’s age was seven times that of his son. What are their present ages?

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 13

Ex 3.3 Class 10 Maths Question 2.
Solve 2x + 3y = 11 and 2x – 4y = -24 and hence find the value of’m’ for which y = mx +3.
Solution:

Accepted Answer

Worksheets for Class 10 Maths

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 14

Ex 3.4 Class 10 Maths Question 1.
Solve the following pairs of linear equations by the elimination method and the substitution method:

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 15

Ex 3.4 Class 10 Maths Question 2.
Form the pair of linear equations for the following problems and find their solutions (if they exist) by the elimination method:
(i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac { 1 }{ 2 }$, if we only add 1 to the denominator. What is the fraction?
(ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
(iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
(iv) Meena went to a bank to withdraw ₹2000. She asked the cashier to give her ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹50 and ₹100 she received.
(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹ 27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

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Question 16

Ex 3.5 Class 10 Maths Question 1.
Which of the following pairs of linear equations has unique solution, no solution or infinitely many solutions. In case there is unique solution, find it by using cross-multiplication method.
(i) x – 3y – 3 = 0, 3x – 9y – 2 = 0
(ii) 2x + y = 5, 3x + 2y = 8
(iii) 3x – 5y = 20, 6x – 10y = 40
(iv) x – 3y – 7 = 0, 3x – 3y – 15 = 0

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
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  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 17

Ex 3.5 Class 10 Maths Question 2.
(i) For which values of a and b does the following pair of linear equations have an infinite number of solutions?
2x + 3y = 7
(a – b)x + (a + b)y = 3a + b – 2
(ii) For which value of k will the following pair of linear equations have no solution?
3x + y = 1
(2k – 1)x + (k – 1)y = (2k + 1)

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 18

Ex 3.5 Class 10 Maths Question 4.
Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
(i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay ₹ 1000 as hostel charges, whereas a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges. Find the fixed charges and the cost of food per day.
(ii) A fraction becomes $\frac { 1 }{ 3 }$ when 1 is subtracted from the numerator and it becomes $\frac { 1 }{ 4 }$ when 8 is added to its denominator. Find the fraction.
(iii) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?
(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 19

Ex 3.5 Class 10 Maths Question 3.
Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x + 5y = 9, 3x + 2y = 4

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Question 20

Ex 3.6 Class 10 Maths Question 1.
Solve the following pairs of equations by reducing them to a pair of linear equations:

Accepted Answer

Pair of Linear Equations - CBSE Class 10 | CBSE Class 10 Maths | Bright Tutorials

BRIGHT TUTORIALS

BRIGHT TUTORIALSCBSE Class X | Academic Year 2026-2027
    
    9403781999Excellence in Education
  
  Mathematics | Pair of Linear EquationsWeb Content
  
    CBSE Class 10 Pair of Linear Equations &mdash; Complete Guide
    This chapter carries 5-6 marks and is crucial for the Algebra unit. Master graphical and algebraic methods for solving pairs of linear equations.

Quick Revision: Key Concepts
    
      Unique solution: a1/a2 &ne; b1/b2 (intersecting lines)
      Infinite solutions: a1/a2 = b1/b2 = c1/c2 (coincident lines)
      No solution: a1/a2 = b1/b2 &ne; c1/c2 (parallel lines)
      Methods: Substitution, Elimination, Cross-multiplication
      Reducible equations: Substitute u = 1/x, v = 1/y

Most Important Questions
    
      Determine consistency of a system of equations
      Solve using elimination or substitution method
      Word problems: age, speed, fraction, geometry type
      Equations reducible to linear form (1/x, 1/y type)

About Bright Tutorials
      Bright Tutorials, Hariom Nagar, Nashik Road, provides expert coaching for CBSE and ICSE students. Our experienced faculty ensures comprehensive preparation for board exams with personalised attention and 3-tier differentiation for students of all levels. Contact us at 9403781999 or visit brighttutorials.in.

Bright Tutorials | Hariom Nagar, Nashik Road | 9403781999 | brighttutorials.in

Pair of Linear Equations in Two Variables

Ex 3.1

Ex 3.2

Ex 3.3

Ex 3.4

Ex 3.5

Ex 3.6

Ex 3.7