Introduction

In earlier classes, you have studied linear equations in one variable. Can you write down a linear equation in one variable ? You may say that:

x + 1 = 0 ,

x + 2 = 0 and

2 y + 3 = 0

are examples of linear equations in one variable.

You also know that such equations have a unique (i.e., one and only one) solution. You may also remember how to represent the solution on a number line. In this chapter, the knowledge of linear equations in one variable shall be recalled and extended to that of two variables.

You will be considering questions like: Does a linear equation in two variables have a solution? If yes, is it unique? What does the solution look like on the Cartesian plane? You shall also use the concepts you studied in Chapter 3 to answer these questions.

Let’s look at the solutions of some linear equations in two variables. Consider the equation 2x + 3y = 5. There are two variables in this equation, x and y.

Scenario 1:Let’s substitute x = 1 and y = 1 in the Left Hand Side (LHS) of the equation. Hence, 2(1) + 3(1) = + = = RHS (Right Hand Side).

Therefore, x = 1 and y = 1 is a solution of the equation 2x + 3y = 5.

Scenario 2:Let’s substitute x = 1 and y = 7 in the LHS of the equation. Hence, 2(1) + 3(7) = 2 + 21 = ≠ RHS.

Therefore, x = 1 and y = 7 is not a solution of the equation 2x + 3y = 5.

Geometrically, this means that the point (1, 1) lies on the line representing the equation 2x + 3y = 5. Also, the point (1, 7) does not lie on this line.