Question

The graph shows some solutions to 2x + y ≤ 10.

Which of these other points is also a solution?
(6.0)
(3.3)

Explain your thinking.
Both
Neither

Answer 1

Answer: (3,3) only

Step-by-step explanation

The point (6,0) means that x = 6 and y = 0 pair up together.

Plug those values into the inequality.

2x + y ≤ 10

2*6 + 0 ≤ 10

12 ≤ 10

We get a false statement at the end, so 2x + y ≤ 10 is false for the point (6,0). Visually, the point is not in the shaded region. It's also not on the boundary either. Refer to the graph below.

Let's try (3,3) now

2x + y ≤ 10

2*3 + 3 ≤ 10

9 ≤ 10

This statement is true, so the original inequality is also true for these x and y values. This point is considered a solution. It is in the shaded region.

See below.