Question

Determine if each of the following are solutions to the inequality y s 5x – 2.swork in the space below each problem.

Answer 1

1. (5, 0) is a solution to the inequality

2. (-2, 6) is not a solution to the inequality

Step-by-step explanation:

Given the inequality

`y\leq5x-2`

We want to check if

1. (5, 0)

2. (-2, 6)

are solutions.

1. (5, 0)

Here, x = 5, y = 0

Insert these in the inequality, evaluate and see if the inequality is satisfied.

`\begin{gathered} 0\leq5(5)-2 \\ 0\leq25-2 \\ 0\leq23 \end{gathered}`

This is true, 0 is less than 23.

Hence, (5, 0) is a solution to the inequality

2. (-2, 6)

Here, x = -2, y = 6

`\begin{gathered} 6\leq5(-2)-2 \\ 6\leq-10-2 \\ 6\leq-12 \end{gathered}`

This is not true, 6 is neither less nor equal to -12

Hence, (-2, 6) is not a solution to the inequality.