Question

Which graph represents the solution set of the system of inequalities?

y<2/3x

y≥−x+2

Answer 1

Bottom right graph

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 < (2)/(3)x \\ \\ 0 ≮ 0`[We shade the portion of the graph that does not contain the origin, which is the right side.]

`\displaystyle y ≥ -x + 2 \\ \\ 0 ≱ 2`[We shade the portion of the graph that does not contain the origin, which is the right side.]

So, now that we got that all cleared up, we can tell that the graphs share a region in between each other ALL ON THE RIGHT SIDE, and that the bottom inequality has a NEGATIVE RATE OF CHANGE [SLOPE], and the top inequality has a POSITIVE RATE OF CHANGE [SLOPE]. Therefore the bottom right graph matches what we want.

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