Question

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

Answer 1

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.