We'll first convert the mixed fractions to "improper" and then get their product, since the area of a rectangle is the product of its length and width.
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Let's convert these inequalities to Slope Intercept Form so that we can graph them easily.
<span>−10x − 5y ≥ 15
Add 10x to both sides.
-5y </span>≥ 10x + 15
Divide both sides by -5 and flip the inequality sign.
y <span>≤ -2x - 3
</span><span>x + y ≤ − 1
Subtract x from both sides.
</span><span>y ≤ -x − 1
When graphed, the solutions lay in Quadrants II, III, and IV. You can see this in the picture I've included.</span>
<span>−10x − 5y ≥ 15
Add 10x to both sides.
-5y </span>≥ 10x + 15
Divide both sides by -5 and flip the inequality sign.
y <span>≤ -2x - 3
</span><span>x + y ≤ − 1
Subtract x from both sides.
</span><span>y ≤ -x − 1
When graphed, the solutions lay in Quadrants II, III, and IV. You can see this in the picture I've included.</span>