How do you solve this system of equations: #5x - 2y < - 6 and x + 2y \geq - 6#?

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Answer 1 · 2017-12-02T21:17:15

See picture and explanation below.

We can solve a system of inequalities by graphing the inequalities and seeing where they both are true.

First we have to convert both inequalities to slope-intercept form, #y=mx=b#.

First inequality:

#5x-2y<-6#

#\implies -2y<-5x-6#

#\implies \underbrace{y>\frac{5}{2}x+3}_{\text{flip the inequality sign}}#

Now the second inequality:

#x+2y\geq -6#

#\implies 2y\geq -x-6#

#\implies y\geq -\frac{1}{2}x-3#

Since we have both inequalities in slope intercept form, we can graph both of them:

Deamos

The area shaded purple is the solution.