# How do you solve 2x-y>=2 and x-2y>=2?

Jul 23, 2015

Solve system of linear inequalities in 2 variables:
(1) $2 x - y \ge 2$
(2) $x - 2 y \ge 2$

#### Explanation:

(1) --> $y \le 2 x - 2$
(2) --> 2y <= x - 2 --> $y \le \frac{x}{2} - 1$
First, graph the line y1 = 2x - 2 by its 2 intercepts.
Make x = 0 --> y = -2. Make y = 0 --> x = 1.
The solution set of inequality (1) is the area below the line y1. Color or shade it.
Next, graph the line y2 = x/2 - 1. by its 2 intercepts.
The area of inequality (2) is the area below the line y2. Color or shade it.
The compound solution set is the commonly shared area.
NOTE. The 2 lines y1 and y2 are included in the solution set.
graph{2x - 2 [-10, 10, -5, 5]}
graph{x/2 - 1 [-10, 10, -5, 5]}