Question

The boundary lines for the system of inequalities is given in the graph.

y ≥ 2x − 3
y ≤ −x + 2


Which region represents the solution to the system of inequalities?

A)
region A


B)
region B


C)
region C


D)
region D

Answer 1

C.

Explanation:

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Answer 2

C)

region C

Explanation:

We have to use what is called the zero-interval test [test point] in order to figure out which portion of the graph these inequalities share:

`\displaystyle y ≤ -x + 2`

0 ≤ 2 ☑ [We shade the portion of the graph that CONTAIN THE ORIGIN, which is the bottom portion.]

`\displaystyle y ≥ 2x - 3`

0 ≥ −3 ☑ [We shade the portion of the graph that CONTAINS THE ORIGIN, which is the left side.]

So, now that we got that all cleared up, we can tell that both graphs share a region where the ORIGIN IS VISIBLE. Therefore region C matches the above inequalities.

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