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CBSE Class 9 Mathematics Question 9 of 9

Linear Equations in Two Variables — Question 5

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Question

Question 3

Check which of the following are solutions of the equation x – 2y = 4 and which are not:

(i) (0, 2)

(ii) (2, 0)

(iii) (4, 0)

(iv) (2,42)(\sqrt{2}, 4\sqrt{2})

(v) (1, 1)

Answer

(i) Substituting (0, 2), in L.H.S. of the equation x - 2y = 4, we get :

⇒ x - 2y = 0 - 2(2) = 0 - 4 = -4.

Since, L.H.S. ≠ R.H.S.

Hence, (0, 2) is not a solution for equation x – 2y = 4.

(ii) Substituting (2, 0), in L.H.S. of the equation x - 2y = 4, we get :

⇒ x - 2y = 2 - 2(0) = 2 - 0 = 2

Since, L.H.S. ≠ R.H.S.

Hence, (2, 0) is not a solution for equation x – 2y = 4.

(iii) Substituting (4, 0), in L.H.S. of the equation x - 2y = 4, we get :

⇒ x - 2y = 4 - 2(0) = 4 - 0 = 4

Since, L.H.S. = R.H.S.

Hence, (4, 0) is a solution for equation x – 2y = 4.

(iv) Substituting (2,42\sqrt{2}, 4\sqrt{2}), in L.H.S. of the equation x - 2y = 4, we get :

⇒ x - 2y = 2−2(42)=2−82=−72\sqrt{2} - 2(4\sqrt{2}) = \sqrt{2} - 8\sqrt{2} = -7\sqrt{2}.

Since, L.H.S. ≠ R.H.S.

Hence, (2,42)(\sqrt{2}, 4\sqrt{2}) is not a solution for equation x – 2y = 4.

(v) Substituting, (1, 1), in L.H.S. of the equation x - 2y = 4, we get :

⇒ x - 2y = 1 - 2(1) = 1 - 2 = -1

Since, L.H.S. ≠ R.H.S.

Hence, (1, 1) is not a solution for equation x – 2y = 4.

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Mathematics | Linear Equations in Two VariablesWeb Content • Interactive Notes

Linear Equations in Two Variables — Interactive Study Guide

Infinite Solutions

A linear equation in two variables has infinitely many solutions. Each solution is a point on the line. The line extends forever in both directions.

Key Concept: One equation, two unknowns = infinite solutions. You need TWO equations to get a unique solution (Class X topic).

Graphing Made Easy

  1. Rewrite as y = mx + c.
  2. Make a table: choose 3 values of x, calculate y for each.
  3. Plot the 3 points. If they’re collinear, draw the line.

Special Lines

y = 3: Horizontal line, 3 units above x-axis.

x = −2: Vertical line, 2 units left of y-axis.

y = x: Line at 45° through origin.

Quick Self-Check

  1. Is (2, 3) a solution of x + y = 5? (Yes: 2 + 3 = 5)
  2. Give 3 solutions of y = 2x. ((0,0), (1,2), (2,4))
  3. What is the equation of the x-axis? (y = 0)

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