Question

How do you solve and graph `2x - 3y > 6` and `5x + 4y < 12`?

Answer 1

Solve and graph system of linear inequalities in 2 variables:
2x - 3y > 6
5x + 4y < 12

Explanation:

Bring the inequalities to standard form:
(1) 2x - 3y - 6 > 0
(2) 5x + 4y - 12 < 0
First, graph Line (1): 2x - 3y - 6 = 0 by its 2 intercepts.
make x = 0 --> y = -3. Make y = 0 --> x = 3.
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 -6 > 0> Not true. Then, the solution is the area that doesn't contain O. Color or shade it.
Next, graph the Line (2): 5x + 4y < 12 by its 2 intercepts. Use O as test point. We get -12 < 0. True. Then, the solution set is the area containing O. Color it.
The compound solution set is the commonly shared area.
graph{2x - 3y - 6 = 0 [-10, 10, -5, 5]}
graph{5x + 4y - 12 = 0 [-10, 10, -5, 5]}