Question

remaining seats to be recliners. if x is the number of stools and y is the number of recliners, which graph represents the solution to the system of inequalities?
$x + y \leq 50$
$x \geq 20$

Explanation:

Step1: Analyze $x \geq 20$

This inequality represents all points to the right of the vertical line $x=20$ (including the line itself, so the line is solid).

Step2: Analyze $x + y \leq 50$

Rewrite in slope-intercept form: $y \leq -x + 50$. This is all points below/on the solid line $y=-x+50$, which has a y-intercept of 50 and x-intercept of 50.

Step3: Find overlapping region

The solution is the area that satisfies both inequalities: right of $x=20$ and below $y=-x+50$.

Answer:

The correct graph is the rightmost graph (third option), which shows the overlapping region of the area to the right of the solid vertical line $x=20$ and below the solid line $x+y=50$.