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CBSE Class 9 Mathematics Question 2 of 9

Linear Equations in Two Variables — Question 3

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Question 2(ii)

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case :

x - y5\dfrac{y}{5} - 10 = 0

Answer

Given,

⇒ x - y5\dfrac{y}{5} - 10 = 0

⇒ (1)x + (−15)y\Big(-\dfrac{1}{5}\Big)y + (-10) = 0

Comparing above equation with ax + by + c = 0, we get :

a = 1, b = -15\dfrac{1}{5} and c = -10

Hence, linear equation : x - y5\dfrac{y}{5} - 10 = 0, a = 1, b = −15-\dfrac{1}{5} and c = -10.

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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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