Question

What’s the answer to this?

Answer 1

Answer:

○ $\displaystyle x > -3 \\ 5y ≥ -4x - 10$

Step-by-step explanation:

This system of inequalities has a shared portion at the origin, so we can easily jump to using the zero-interval test [test point (0, 0)] to verify the inequalities as false or true:

$\displaystyle 5[0] ≥ -4[0] - 10 → 0 ≥ -10$☑

$\displaystyle 0 > -3$☑

Plus, the top inequality has a dashed line ["<" or ">"], and the bottom inequality has a solid line, so this must have an equivalence line underneath each inequality symbol ["≤" or "≥"].

** Hold on though! Although it looks obvious about what the second inequality is, we need to double-check and make sure anyway, just to be on the safe side ☺:

$\displaystyle \frac{5y}{5} ≥ \frac{-4x - 10}{5} → y ≥ -\frac{4}{5}x - 2$

From the y-intercept of $\displaystyle [0, -2],$we do $\displaystyle \frac{rise}{run}$by either moving four blocks north over five blocks west or four blocks south over five blocks east [west and south are negatives]. This IS what our solid graph looks like, so we are correct!

So, from all what was explained, you have your answer.

I am joyous to assist you anytime.