Question

Which system of inequalities represents region Z?

Answer 1

The system of inequalities is

`y\geq 3x-2`

`y<-(1/5)x+2`

Explanation:

step 1

Find the equation of the solid blue line

Let

`A(0,-2), B(1,1)`

Find the slope of AB

`m=(1+2)/(1-0)=3`

The equation of the line into slope intercept form is equal to

`y=mx+b`

we have

`m=3`

`b=-2` ----> the point A is the y-intercept

substitute

`y=3x-2` -----> equation of the solid blue line

The solution of the inequality is the shaded area above the solid line

therefore

The first inequality is

`y\geq 3x-2`

step 2

Find the equation of the dashed red line

Let

`C(0,2), D(5,1)`

Find the slope of CD

`m=(1-2)/(5-0)=-1/5`

The equation of the line into slope intercept form is equal to

`y=mx+b`

we have

`m=-1/5`

`b=2` ----> the point C is the y-intercept

substitute

`y=-(1/5)x+2` -----> equation of the dashed red line

The solution of the inequality is the shaded area below the dashed line

therefore

The second inequality is

`y<-(1/5)x+2`

The system of inequalities is

`y\geq 3x-2`

`y<-(1/5)x+2`