# How do you solve the following system?: #y <2x+4, -3x-2y>= 6#

##### 1 Answer

Solution set

#### Explanation:

Bring the 2 inequalities to standard form:

- y + 2x + 4 > 0 (1)

First, graph Líne 1 --> - y + 2x + 4 = 0 by its 2 intercept.

Make x = 0 --> y-intercept = 4

Make y = 0 --> x-intercept = -2

Next, graph Line 2 --> - 2y - 3x - 6 = 0

Make x = 0 --> y-intercept = -3

Make y = 0 --> x-intercept = -2

To find the solution set of inequality (1), replace x = 0 and y = 0 into the inequality (1). We get 4 > 0. It is true. Then the origin (0, 0) is located inside the solution set, that is the area below Line 1.

Replace x = 0 and y = 0 into inequality (2), we get -6 > 0. Not true.

There for, O is outside the solution set, that is below the Line 2.

The solution set of the system is the commonly shared area.

graph{- y + 2x + 4 = 0 [-10, 10, -5, 5]}

graph{- 2y - 3x - 6 = 0 [-10, 10, -5, 5]}