Chapter I : Linear Equations in two variables in two variables

Linear equation in two variables can be written as

and a, b and c are real numbers.

This equation has infinitely many solution. When we consider two linear equation together then we say it a system of two variable x and y. such as.

5x + 3y + 2 = 0
2x - 3y + 5 = 0

Algebraic solution of system of linear equation:

1. Elimination by substitution:

Let us consider a system of linar equations:

From equation (1) we get

x = (1 + 7y)/2

Putting the value of x in e.q. (2) we get

Or, 2 + 14y + 3y = 15

Or, 17y = 13

Or, y = 13/17

Putting value of y in eq (1) we get

Or, 2x = 1 + 91/17

Or, 2x = (17+91)/17

Or, x = 108/34

Or, x = 54/17