Question

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

Answer 1

Solve system of linear inequalities in 2 variables:
(1) `2x - y >= 2`
(2) `x - 2y >= 2`

Explanation:

(1) --> `y <= 2x - 2`
(2) --> 2y <= x - 2 --> `y <= 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]}