Question

A new coffee shop can hold no more than 50 seats. The owner wants at least 20 of the seats to be stools and the 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 ≤ 50

x ≥ 20

On a coordinate plane, 2 solid straight lines are shown. The first line is horizontal to the y-axis at y = 20. Everything below the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the left of the line is shaded.

On a coordinate plane, 2 solid straight lines are shown. The first line is vertical to the x-axis at x = 20. Everything to the left of the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the right of the line is shaded.

On a coordinate plane, 2 solid straight lines are shown. The first line is horizontal to the y-axis at y = 20. Everything above the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the left of the line is shaded.

On a coordinate plane, 2 solid straight lines are shown. The first line is vertical to the x-axis at x = 20. Everything to the right of the line is shaded. The second line has a negative slope and goes through (0, 50) and (50, 0). Everything to the left of the line is shaded.

Answer 1

The correct graph is the fourth option.

Reason: x ≥ 20 is the vertical line x = 20 with the region to the right shaded. x + y ≤ 50 is the line through (0,50) and (50,0) (solid because ≤) with the region containing the origin shaded (below/left of the line). The solution is the intersection: right of x = 20 and below the line, which is the fourth graph.