Mathematics · Class 9
Linear Equations in Two Variables
Graphical and algebraic methods for pairs of linear equations.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
A linear equation in two variables has the form ax + by + c = 0 where a, b are not both zero. Solutions are ordered pairs; infinitely many solutions exist, and their graph is a straight line.
Standard Form and Solutions
- General form: ax + by + c = 0 (a, b not both 0)
- A solution (x, y) satisfies the equation
- Every point on the line is a solution
- x = k is vertical line; y = k is horizontal line
Graphing
- Find two solutions and plot them
- Join points to get the line
- Intercepts: set y = 0 for x-intercept; x = 0 for y-intercept
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Find solutions
Find two solutions of 2x + y = 6.
- 1If x = 0, y = 6 → (0, 6)
- 2If x = 3, y = 0 → (3, 0)
Answer
(0, 6) and (3, 0) among infinitely many
Example 2: Check solution
Is (2, 1) a solution of x − 2y = 0?
- 1Substitute: 2 − 2(1) = 0
- 20 = 0 ✓
Answer
Yes, (2, 1) is a solution
Key Points to Remember
- ✓ Infinitely many solutions for one equation
- ✓ Graph of ax + by + c = 0 is a straight line
- ✓ Two distinct points determine the line
Exam Tips
- • Find at least two points before drawing
- • Label axes and scale on graph
- • Verify solutions by substitution
Practice MCQs — Linear Equations in Two Variables
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
2x + 3y = 12 is a: