Question

Which graph represents the solution set of the system of inequalities?

{y≥12x+1y>−x−2



A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region above the solid line and above the dashed line is shaded.

A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 4 comma 3 end ordered pair. The region above the solid line and above the dashed line is shaded.

A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 2 comma negative 4 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.

A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.

Answer 1

The graphs are in comment.

The system of equation is:

{y<2x+2x+y≥−3{y<2x+2x+y≥−3

Hence, the two lines defining the solution set are y=2x+2y=2x+2 and y=−x−3y=−x−3, which are the lines drawn in both A and C.

In addition, we are looking for a solution set such as y<2x+2y<2x+2, which means the set should be below the increasing line. The only solution remaining is hence C.

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