Question

A system of linear inequalities is below. Which point is NOT a solution to this system?

Answer 1

INFORMATION:

We have the next system of linear inequalities

`\begin{cases}3x-y\leq2{} \\ x+7y\leq{4}\end{cases}`

And we must find the point in the options which is not a solution

STEP BY STEP EXPLANATION:

To find it, we must replace the points in the system:

- (0, -1):

`\begin{gathered} 3(0)-(-1)\leq2 \\ 0+1\leq2 \\ 1\leq2 \end{gathered}`

`\begin{gathered} 0+7(-1)\leq4 \\ -7\leq4 \end{gathered}`

The two inequalities are true, so the point (0, -1) is a solution to the system

- (-1, -6):

`\begin{gathered} 3(-1)-(-6)\leq2 \\ -3+6\leq2 \\ 3\leq2 \end{gathered}`

Since 3 ≤ 2 is false, the point (-1, -6) is not a solution to the system

ANSWER:

(-1, -6)