Question

How do you graph `2x - 3y >=9` and `- x - 4y >=8`?

Answer 1

Graph and solve system:
(1) `2x - 3y >= 9`
(2) `-x - 4y >= 8`

Explanation:

Bring the inequalities to standard form:
(1) `2x - 3y - 9 >= 0`
(2) `- x - 4y - 8 >= 0`
First, graph Line (1): 2x - 3y - 9 = 0 by its 2 intercepts.
make x = 0 --> y = -2. Make y = 0 --> `x = 9/2`.
To find the solution set, use the origin O as test point. Substitute x = 0, y = 0 into the inequality (1). We get `-9 >= 0`. Not true. Then, the solution set is the area that doesn't contain O. Color or shade it.
Next, graph the Line (2): -x - 4y - 8 = 0 by its 2 intercepts.
Make x = 0 --> y = -2. Make y = 0 --> x = -8.
Substitute x = 0 and y = 0 into inequality (2). We get `-8 >= 0.` Not true. Then, the solution set is the area that doesn't contain O. Color or shade it.
The compound solution set is the commonly shared area.
graph{2x - 3y - 9 = 0 [-10, 10, -5, 5]}
graph{-x - 4y - 8 = 0 [-10, 10, -5, 5]}
NOTE, The 2 lines (1) and (2) are included in the solution set.