Question

How do you graph `10x+6y<30` and `5x-10y>30`?

Answer 1

Graph system of linear equations in 2 variables:
(1) 10 x + 6y - 30 < 0
(2) 5x - 10 y - 30 > 0

Explanation:

First graph Line (1) -> 10 x + 6y - 30 = 0 by its 2 intercepts.
Make x = 0 -> y = 5; Make y = 0, --> x = 3.
Find the solution set of (1). Use origin O as test point. Substitute x = 0 and y = 0 into (1), we get: -30 < 0. It is true, then the area containing O is the solution set. Color or shade it.
Next, graph Line (2) -> 5x - 10y - 30 = 0 by its 2 intercepts.
Use O as test point. We get: - 30 > 0. Not true. Then, the area, not containing O, is the solution set. Color or shade it.
The compound solution set is the commonly shared area.
graph{10x + 6y - 30 = 0 [-10, 10, -5, 5]}
graph{5x - 10y - 30 = 0 [-10, 10, -5, 5]}