Question

Which system of inequalities represents region Z?

Answer 1

Answer:

The system of inequalities is

$y\geq 3x-2$

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

Step-by-step 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

$y\geq 3x-2$

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