Question

How do you sketch the solution for the system of inequalities `y<=-x-2` and `y>=-5x+2`?

Answer 1

`y <= - x - 2` (1)
`y >= - 5x + 2` (2)
First graph the 2 linear functions by intercepts:

a. y1 = - x - 2
Make x = 0 --> y-intercept is -2
Make y = 0 --> x-intercept is - 2
b. y2 = -5x + 2
Make x = 0 --> y-intercept is 2
Make y = 0 --> x-intercept is `2/5`
Graphically solve the 2 linear inequalities (1) and (2).
The solution set of (1) is the area below the line y1. Color it.
The solution set of (2) is the area above the line y2. Color it.
The combined solution set of the system is the area commonly shared by the 2 above solution set areas.
graph{-x - 2 [-10, 10, -5, 5]}
graph{-5x + 2 [-10, 10, -5, 5]}