Question

$-x + 4y < -24$
enter three different points, separated by commas, that are solutions to the system of inequalities.
enter three different points, separated by commas, that are not solutions to the system of inequalities.

Explanation:

Step1: Rewrite inequality for clarity

Rearrange $-x + 4y < -24$ to $4y < x - 24$, so $y < \frac{x - 24}{4}$

Step2: Test points for solutions

Pick $x=32$: $y < \frac{32-24}{4}=2$. Use $(32,0)$: $-32 + 4(0)=-32 < -24$, valid.
Pick $x=40$: $y < \frac{40-24}{4}=4$. Use $(40,1)$: $-40 + 4(1)=-36 < -24$, valid.
Pick $x=28$: $y < \frac{28-24}{4}=1$. Use $(28,-1)$: $-28 + 4(-1)=-32 < -24$, valid.

Step3: Test points for non-solutions

Pick $x=0$: $y < \frac{0-24}{4}=-6$. Use $(0,0)$: $-0 + 4(0)=0
less -24$, invalid.
Pick $x=24$: $y < \frac{24-24}{4}=0$. Use $(24,1)$: $-24 + 4(1)=-20
less -24$, invalid.
Pick $x=12$: $y < \frac{12-24}{4}=-3$. Use $(12,0)$: $-12 + 4(0)=-12
less -24$, invalid.

Answer:

Solutions: $(32, 0), (40, 1), (28, -1)$
Non-solutions: $(0, 0), (24, 1), (12, 0)$