# How do you graph 2x + 3y < 9 and 7x + 3y < -6?

Jul 24, 2015

Graph system of 2 linear inequalities
2x + 3y < 9
7x + 3y < - 6

#### Explanation:

Bring these inequalities to standard form:
(1) 2x + 3y - 9 < 0
(2) 7x + 3y + 6 < 0
First graph the line y1 -> 2x + 3y - 9 = 0 by its e intercepts.
Make x = 0 -> y = 3. Make y = 0 -> x = 9/2.
To find the solution set of inequality (1), use the origin O as test point. Replace x = 0 and y = 0 into (1), we get -9 < 0. True. Then, the solution set of (1) is the area that contains O. Color or shade it.
Next, graph Line y2 -> 7x + 3y + 6 = 0 by its 2 intercepts.
Make x = 0 -> y = -2. Make y = 0 -> x = -6/7.
Replace x = 0 and y = 0 into inequality (2) --> 6 < 0. It is 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{7x + 3y + 6 = 0 [-10, 10, -5, 5]}