# How do you graph the system #-3x+2y>3# and #x+4y<-2#?

##### 1 Answer

Jun 30, 2015

Solve the system

(1) -3x + 2y > 3

(2) x + 4y < -2

#### Explanation:

First, bring the 2 inequalities to standard form:

(1) -3x + 2y - 3 > 0

(2) x + 4y + 2 < 0

Graph the Line (1): f(x, y) = -3x + 2y - 3 by its two intercepts.

Make x = 0 --> y = 3/2 . Make y = 0, --> x = -1.

Use test point origin O(0, 0). We get -3 > 0 . Not true. Then the area that doesn't contain O, is the solution set. Color or shade this area.

Next graph the Line (2): f(x, y) = x + 4y - 2 by its 2 intercepts.

Make x = 0 --> y = -1/2. make y = 0, --> x = - 2

Test point origin O(0, 0). We get: 2 < 0. Not true. Then the area, not containing O, is the solution set. Shade or color it.

The combined solution set is the commonly shared area.