Question

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

Answer 1

Solution set

Explanation:

Bring the 2 inequalities to standard form:
- y + 2x + 4 > 0 (1)
`-2y - 3x - 6 >= 0` (2).
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]}