Question

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

Answer 1

See picture and explanation below.

Explanation:

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:

The area shaded purple is the solution.