Class 9 Mathematics
Chapter 4: Linear Equations in Two Variables
Exercise 4.2 – Stepwise Solutions
Important Concept
A linear equation in two variables has infinitely many solutions because it represents a straight line.
Q1. Which one of the following options is true, and why?
Given equation: y = 3x + 5
This is a linear equation in two variables.
For every value of x, we get a corresponding value of y.
Answer: (iii) Infinitely many solutions
Q2. Write four solutions for each of the following equations
(i) 2x + y = 7
y = 7 − 2x
Solutions:
(0, 7), (1, 5), (2, 3), (3, 1)
(ii) πx + y = 9
y = 9 − πx
Solutions:
(0, 9), (1, 9 − π), (2, 9 − 2π), (3, 9 − 3π)
(iii) x = 4y
Solutions:
(0, 0), (4, 1), (8, 2), (12, 3)
Q3. Check which of the following are solutions of x − 2y = 4
Substitute each pair:
(i) (0, 2)
0 − 4 = −4 ≠ 4 → Not a solution
(ii) (2, 0)
2 − 0 = 2 ≠ 4 → Not a solution
(iii) (4, 0)
4 − 0 = 4 → Solution
(iv) (√2, 4√2)
√2 − 8√2 = −7√2 ≠ 4 → Not a solution
(v) (1, 1)
1 − 2 = −1 ≠ 4 → Not a solution
Q4. Find the value of k
Given: x = 2, y = 1 is a solution of 2x + 3y = k
Substitute values:
k = 2(2) + 3(1)
k = 4 + 3 = 7
Answer: k = 7