Question

which point would be a solution to the system of linear inequalities shown below?
$y \geq -x - 8$ $y > -\frac{6}{5}x + 4$
answer attempt 1 out of 2
$(-5, 10)$ $(10, -10)$
$(0, -8)$ $(5, 8)$

Explanation:

Step1: Test (-5,10) in first inequality

Substitute $x=-5, y=10$ into $y \geq -x -8$:
$10 \geq -(-5) -8 = 5 -8 = -3$
This is true.

Step2: Test (-5,10) in second inequality

Substitute $x=-5, y=10$ into $y > -\frac{6}{5}x +4$:
$10 > -\frac{6}{5}(-5) +4 = 6 +4 = 10$
This is false ($10$ is not greater than $10$).

Step3: Test (0,-8) in first inequality

Substitute $x=0, y=-8$ into $y \geq -x -8$:
$-8 \geq -0 -8 = -8$
This is true.

Step4: Test (0,-8) in second inequality

Substitute $x=0, y=-8$ into $y > -\frac{6}{5}x +4$:
$-8 > -\frac{6}{5}(0) +4 = 4$
This is false.

Step5: Test (10,-10) in first inequality

Substitute $x=10, y=-10$ into $y \geq -x -8$:
$-10 \geq -10 -8 = -18$
This is true.

Step6: Test (10,-10) in second inequality

Substitute $x=10, y=-10$ into $y > -\frac{6}{5}x +4$:
$-10 > -\frac{6}{5}(10) +4 = -12 +4 = -8$
This is false ($-10$ is not greater than $-8$).

Step7: Test (5,8) in first inequality

Substitute $x=5, y=8$ into $y \geq -x -8$:
$8 \geq -5 -8 = -13$
This is true.

Step8: Test (5,8) in second inequality

Substitute $x=5, y=8$ into $y > -\frac{6}{5}x +4$:
$8 > -\frac{6}{5}(5) +4 = -6 +4 = -2$
This is true.

Answer:

(5, 8)