Question

Identify point in region of inequalities Below are two inequalities and the graphs of their lines without the shading. By imagining where the shading should be, identify which point would satisfy BOTH inequalities.y > - x - 5 y > x -3

Answer 1

Only (2, 7) is a point that would satisfy both inequalities among the given options.

Step-by-step explanation

The shaded region now depends on whether the inequality sign is facing y or not.

If the inequality sign is facing y, it means numbers above the line plotted are the wanted region and the upper part of the graph is shaded.

If the inequality sign is not facing y, it means numbers below the line plotted are the wanted region and the lower part of the graph is shaded.

For the two inequalities, the inequality sign is facing the y, so, the shaded area will be the upper part of both of these graphs.

Then the solution will be the regions that they have in common.

We can see that the wanted region starts from where the two lines intersect at y = -4 upwards, without going out of each of the two lines.

So, checking the points given one at a time,

(2, 7)

This point on the graph is solidly in the wanted region described.

(-1, -10)

This point is below the point of intersection and is visibly not in the wanted, shaded region.

(10, -6)

This point too is not in the wanted region as that point falls way below the wanted region.

(-5, -4)

This region too is not in the wanted region.

Hope this Helps!!!