Question

−10x − 5y ≥ 15 x + y ≤ −1 what are the quadrants containing a solution to the above system of linear inequalities.

Answer 1

Let's convert these inequalities to Slope Intercept Form so that we can graph them easily.

−10x − 5y ≥ 15
Add 10x to both sides.
-5y ≥ 10x + 15
Divide both sides by -5 and flip the inequality sign.
y ≤ -2x - 3

x + y ≤ − 1
Subtract x from both sides.
y ≤ -x − 1

When graphed, the solutions lay in Quadrants II, III, and IV. You can see this in the picture I've included.