Question

determine whether each point is a solution of the linear inequality.
point (2,-2) linear inequality y≤2x-3

a) no
b) yes

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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.