Which system of linear inequalities is represented by the graph?
x – 5y < –5 and y < –2x – 4
x + 5y > 5 and y < 2x + 4
x – 5y < –5 and y < –2x + 4
x + 5y > 5 and y < 2x – 4

Step 1

Find the equation of the inequality of the solid red line

we know that

the equation of red the line is

The solution is the shaded area above the solid line (see the given graph)

therefore

the inequality is equal to

Step 2

Find the equation of the inequality of the solid blue line

we know that

the equation of the blue line is

The solution is the shaded area below the solid line (see the given graph)

therefore

the inequality is equal to

therefore

the answer is

The system of linear inequalities is equal to

and

using a graphing tool

the solution of the system is the shaded area in the attached figure