The graph below represents which system of inequalities?

graph of two infinite lines that intersect at a point. one line is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line. the other line is solid, and goes through the points 1, 1, 2, negative 1 and is shaded in below the line.

The system of inequalities is

and

The solution is the shaded green area

Step-by-step explanation:

step 1

Find the equation of the inequality A

The line is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line

Find the slope

(-3,0),(-4,-1)

m=(-1-0)/(-4+3)=1

The equation of the line is y=mx+b

we have

m=1

b=3 ----> the y-intercept (see the graph)

substitute

y=x+3 -----> equation of the solid line A

The equation of the inequality is

-----> inequality A

step 2

Find the equation of the inequality B

The line is solid and goes through the points 1, 1, 2, negative 1 and is shaded in below the line

Find the slope

(1,1),(2,-1)

m=(-1-1)/(2-1)=-2

The equation of the line is y=mx+b

we have

m=-2

b=3 ----> the y-intercept (see the graph)

substitute

y=-2x+3 -----> equation of the solid line B

The equation of the inequality is

-----> inequality B

therefore

The system of inequalities is

-----> inequality A

-----> inequality B

The solution is the shaded green area

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step-by-step explanation:

step-by-step explanation:

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