Question

What is the coordinate of the point in the solution set?

Answer 1

Answer:  (-7, 4)

Other solutions are possible.

=====================================================

Explanation:

The dashed line is $y = \frac{1}{2}x+6$. We shade above this dashed line to draw the region for $y > \frac{1}{2}x+6$. This region is shown in green and also the gray region as well.

The purple and gray region is $y \le -\frac{3}{2}x-2$ which consists of the solid boundary line $y = -\frac{3}{2}x-2$ and stuff below it.

When considering both inequalities at the same time, we shade above the dashed line and below the solid line to get the gray region only.

This gray region is the solution set of the system of inequalities. Pick any point from this region to get the final answer.

One such point is (-7, 4). There are infinitely many other possible answers.

To verify that point, plug in the coordinates into each inequality. When simplifying, you should get a true statement.