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

##### 1 Answer

Jul 11, 2015

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]}