Is (–4, 7) a solution to this system of inequalities? y < 7 y > 1 2 x − 2

Answer 1

To determine if (-4, 7) is a solution to the system of inequalities, we need to check if it satisfies both inequalities.

The first inequality is y < 7. Plugging in (-4, 7):

7 < 7

This statement is false, so (-4, 7) does not satisfy y < 7.

The second inequality is y > 1/2x - 2. Plugging in (-4, 7):

7 > 1/2(-4) - 2
7 > -2 - 2
7 > -4

This statement is true, so (-4, 7) satisfies y > 1/2x - 2.

Since (-4, 7) does not satisfy y < 7 but satisfies y > 1/2x - 2, it is not a solution to the system of inequalities.