Linear equations in two variables with examples

An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear.An equation whose graph is a straight line is called a linear equation. (linear means straight). An equation of degree one is linear.

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

Example:

2x + 3y = 5, x - 2y = 6, -6x + y =8

A pair of values of x and y that satisfy a given linear equation in two variables is said to be its solution.

Example:

x = 1, y = 1 is a solution of 2x + 3y = 5

2(1) + 3(1) = 5

x = -2, y = 3 is also a solution of 2x + 3y = 5

2(-2) + 3(3) = 5

-4 + 9 = 5

Similarly, we can find many more solutions for 2x + 3y = 5

A linear equation in two variables has infinitely many solutions.

Example 1:

Find four solutions of the equation 2x + y = 5.

Suggested answer:

2x + y = 5

y = 5 - 2x

Put x = 0, y = 5

x = 1, y = 5 - 2 = 3

x = 2, y = 5 - 4 = 1

x = 3, y = 5 - 6 = -1