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.

How do you solve this system of equations: 5x - 2y < - 6 and x + 2y \geq - 65x - 2y < - 6 and x + 2y \geq - 6?