A linear equation in two variables is of the form ax + by + c = 0, where
a. a ≠ 0, b ≠ 0
b. a = 0, b ≠ 0
c. a ≠ 0, b = 0
d. a = 0, c = 0

Solution:

We know that

An equation is a statement in which one expression equals another expression.

The process of finding solution(s) is called solving an equation.

An equation of the form ax + by + c = 0, where a, b and c are real numbers such that a ≠ 0 and b ≠ 0, is called a linear equation in two variables.

Therefore, a linear equation in two variables is of the form ax + by + c = 0, where a ≠ 0, b ≠ 0.

✦ Try This: The linear equation 2x - y = 3x - 4 has : a. A unique solution, b. Two solutions, c. Infinitely many solutions, d. No solution

Given

2x - y = 3x - 4

By rearranging

3x - 2x + y - 4 = 0

x + y - 1 = 0

So we get

y = 1 - x

Here we will get different values of y for various x values

Therefore, the linear equation has infinitely many solutions.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 4

NCERT Exemplar Class 9 Maths Exercise 4.1 Sample Problem 2

A linear equation in two variables is of the form ax + by + c = 0, where a. a ≠ 0, b ≠ 0, b. a = 0, b ≠ 0, c. a ≠ 0, b = 0, d. a = 0, c = 0

Summary:

A linear equation in two variables is of the form ax + by + c = 0, where a ≠ 0, b ≠ 0

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