Question

What is the system of inequalities associated with the following graph?

A. x + y >2
2x - y < 1

B. x + y < 2
2x - y > 1

C. x + y > 2
2x - y > 1

D. x + y < 2
2x - y < 1

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Answer 1

This leads to C: x + y > 2 and 2x - y > 1

Explanation:

All of the answer options have the same structure, with the exception of the < and > signs. We can assume the the two lines on the graph conform to the line defined by:

x + y =2, and

2x - y = 1

See the attached graph. The lines y = -x+2 and y = 2x-1 match the provided graph.

But the equations are all inequalities. So the darker areas represent the possibilities of values for x and y. The darkeest area is where the solutions for both equations overlap, so look for equations that would satisfy that situation. As shown, the equations are:

y<2x-1, and

y>-x+2

Rearrange these to match the options:

y-2x < -1, and

y + x > 2

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Note that y-2x < -1 is the same as 2x-y > 1

This leads to C: x + y > 2 and 2x - y > 1