Choose the system of inequalities whose solution is represented by the graph.

  -x + y > -4; x + y < 3 . . . . . last choice

Step-by-step explanation:

The boundary lines are both dashed, so there will be no "or equal to" as part of the inequality symbols (eliminates the second choice).

The downward sloping line has x- and y-intercepts that are both 3, so it will have the equation in intercept form ...

  x/3 + y/3 = 1

Multiplying by 3 gives x+y=3. The shading is below it, so the inequality with that line as the boundary is ...

  x + y < 3

This inequality is only part of the last choice.

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The upward sloping line has x- and y- intercepts of 4 and -4, so its equation in intercept form is ...

  x/4 + y/-4 = 1

Multiplying by -4 gives -x+y=-4. The shading is above it, so the inequality with that boundary line is ...

  -x + y > -4

This inequality is included in the last choice.