Pair of linear equations in two variables (ସରଳ ସମୀକରଣ)odia medium class 10 mathematics ch-1, part-1

Introduction

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) = 2 + 3 = 5 = RHS (Right Hand Side). Hence, we can conclude that x = 1 and y = 1 is a solution of the equation 2x + 3y = 5. 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 = 23 ≠ 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. In simple words, every solution of the equation is a point on the line representing it.

To generalize, each solution (x, y) of a linear equation in two variables, ax + by + c = 0, corresponds to a point on the line representing the equation, and vice versa.