y > -½ x + a

y > 2 x – a

If the value of a is 7, which of the following is a possible solution to the system of inequalities above?

A) (2, 6)
B) (4, 5)
C) (5, 4)
D) (5, 3)

Is there a better way than plugging in the answers to solve this?

Hm. Exactly as written, there’s no answer here. Is the first inequality really a less than?

Generally speaking, though, a graph can be very clarifying for questions like this. Here’s the graph as provided:

You’d be looking for a point in the purple area, but as you can see none of the answer choices are in there (on the dotted line doesn’t count). However, if we change the first inequality to less than, then C is correct:

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