Question

How do you graph `5x + 3y > -6` and `2y + x < 6`?

Answer 1

Graph system of 2 linear inequalities in 2 variables:
5x + 3y > -6
2y + x < 6

Explanation:

Bring the inequalities to standard form:
(1) 5x + 3y + 6 > 0
(2) 2y + x - 6 < 0
First, graph the Line (1) -> 5x + 3y + 6 = 0 by its 2 intercepts.
Make x = 0 --> y = - 2. Make y = 0 --> x = -6/5.
Use the origin O as test point. Replace x = 0 and y = 0 into inequality (1). We get: 6 > 0. True!. Then, the solution set of inequality (1) is the area containing O. Color it.
Next, graph Line (2) -> 2y + x - 6 = 0 by its 2 intercepts.
Make x = 0 --> y = 3. Make y = 0 --> x = 6.
Use O as test point. The solution set of (2) is the area containing O. Color it.
The compound solution set is the commonly shared area.
graph{5x + 3y + 6 = 0 [-10, 10, -5, 5]}
graph{2y + x - 6 = 0 [-10, 10, -5, 5]}