# Graphing Linear Inequalities

The solution to an inequality with two variables is a half-plane, which is to represent the resulting equation obtained by transforming the inequality into a linear function.

2x + y ≤ 3

1. Transform the inequality into a linear function.

2x + y = 3

2.Give two values to the variables, which creates two points.

x = 0; 2 · 0 + y = 3; y = 3; (0, 3)

x = 1; 2 · 1 + y = 3; y = 1; (1, 1)

3. Represent and join these points with a straight line.

4. Take a point, for example (0, 0). Place these values in the inequality. If it is true, the solution is the half plane through the point, otherwise the solution will be the other half plane.

2x + y ≤ 3

2 · 0 + 0 ≤ 3 0 ≤ 3 Yes

2x + y > 3

2 · 0 + 0 > 3 ;0 > 3 **No **

In this case (greater than, but not equal) the points of the straight line do not belong to the solution.