Question

Give the coordinates of one point in the solution set.

Answer 1

Point (0, 0) satisfies the inequalities

Explanation:

Sometimes graphing is the best way to determine where the region is that satisfies both inequalities. Then you can choose a point accordingly

The graph of both inequalities is attached. The heavily shaded region in blue represents the region that satisfies both inequalities

If you look at the graph, you can see that (0, 0) falls in the heavily shaded region and therefore it satisfies both constraints

Indeed at (0, 0)

7(0) + 2(0) = 0 which is > -4 since 0 is greater than all negative numbers

Also
-5(0) + 6(0) = 0 which is indeed ≤ 6

So one point is (0, 0)