Question

identify the graph and describe the solution set of this system of inequalities y<-3/2x-10, y>-3/2x-2

Answer 1

The system has no solution

Explanation:

we have

`y < -(3)/(2)x-10` ----> inequality A

The solution of the inequality A is the shaded area below the dashed line
`y=-(3)/(2)x-10`

The slope of the dashed line is negative

The y-intercept of the dashed line is -10

The x-intercept of the dashed line is -20/3

`y > -(3)/(2)x-2` ----> inequality B

The solution of the inequality B is the shaded area above the dashed line
`y=-(3)/(2)x-2`

The slope of the dashed line is negative

The y-intercept of the dashed line is -2

The x-intercept of the dashed line is -4/3

Using a graphing tool

The dashed lines are parallel

therefore

The system has no solution

see the attached figure