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

Jul 23, 2015

Graph and solve system:
(1) $2 x - 3 y \ge 9$
(2) $- x - 4 y \ge 8$

#### Explanation:

Bring the inequalities to standard form:
(1) $2 x - 3 y - 9 \ge 0$
(2) $- x - 4 y - 8 \ge 0$
First, graph Line (1): 2x - 3y - 9 = 0 by its 2 intercepts.
make x = 0 --> y = -2. Make y = 0 --> $x = \frac{9}{2}$.
To find the solution set, use the origin O as test point. Substitute x = 0, y = 0 into the inequality (1). We get $- 9 \ge 0$. 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 $- 8 \ge 0.$ 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.