Question

Determine whether each point is a solution of the linear inequality.

point (2,-2) linear inequality y≤2x-3

a) no
b) yes

​

Answer 1

Given:

The inequality is

`y\leq 2x-3`

The point is (2,-2).

To find:

Whether the given point is a solution of the given linear inequality or not.

Solution:

If the given point satisfy the given inequality, then it is a solution of the linear inequality.

We have,

`y\leq 2x-3`

To check the point (2,-2), substitute x=2 and y=-2 in the above equality.

`-2\leq 2(2)-3`

`-2\leq 4-3`

`-2\leq 1`

We know that -2 is less than 1. So, the statement
`-2\leq 1` is true. It means the point (2,-2) satisfy the given inequality.

Therefore, yes, the point (2,-2) is a solution of the linear inequality and the correct option is b.