Consider this system of inequalities. x plus y is less than or equal to negative 3 y is less than x over 2 Which graph shows the solution for this system?

Answer

A

Image with description On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (negative 3 comma 0) and (0 comma negative 3). Everything to the left of the line is shaded. The second solid line has a positive slope and goes through (negative 2 comma negative 1) and (0 comma 0). Everything to the right of the line is shaded.

B

Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 3 comma 0) and (0 comma negative 3). Everything to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 2 comma negative 1) and (0 comma 0). Everything to the left of the line is shaded.

C

Image with description On a coordinate plane, 2 straight lines are shown. The first dashed line has a negative slope and goes through (negative 3 comma 0) and (0 comma negative 3). Everything to the left of the line is shaded. The second solid line has a positive slope and goes through (negative 2 comma negative 1) and (0 comma 0). Everything to the left of the line is shaded.

D

Image with description On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 3 comma 0) and (0 comma negative 3). Everything to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 2 comma negative 1) and (0 comma 0). Everything to the right of the line is shaded.

Explanation

Rewrite the first inequality as y ≤ −x − 3. Because it includes equality, its boundary is solid; the solution is below the line, which is the left side in the graph description. The second inequality is y < x/2, so its boundary is dashed, and the solution is below that positive-slope line, on its right side. Choice A shows both boundaries and shaded regions correctly.

AI-written and checked against the verified answer.

Pretest

Consider this system of inequalities. x plus y is less than or equal to negative 3 y is less than x over 2 Which graph shows the solution for this system?

Explanation

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