Please Help Asap Its Pre-Calculus The point (−2, 2) is a solution to which of the following systems?

y > −2x + 2 and y > x + 5
y < x + 2 and y > x − 1
y < 2x + 8 and y ≥ −x − 3
y < 2x + 3 and y ≥ −2x − 5

The point is a solution of the system given by and

Given point:

Given systems:

To find: The system to which the given point is a solution

If a point is a solution of a system, then the coordinates of the point satisfies all the equation(s) or inequation(s) of the system. So, we can substitute the x & y coordinates of the given point into the inequalities of each of the given systems and check if the inequalities are satisfied by the coordinates of the point.

(1) and

Substitute the coordinates of the point into the inequalities of the system.

Put in to get,

The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.

This implies that the given point is not a solution of this system.

(2) and

Substitute the coordinates of the point into the inequalities of the system.

Put in to get,

The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.

This implies that the given point is not a solution of this system.

(3) and

Substitute the coordinates of the point into the inequalities of the system.

Put in to get,

This is a true inequality. Then, the given point satisfies the first inequality of the system.

We will now check if the point satisfies the second inequality of the system.

Put in to get,

This is also a true inequality. Then, the given point also satisfies the second inequality of the system.

Thus, the given point is a solution of this system.

(4) and

Substitute the coordinates of the point into the inequalities of the system.

Put in to get,

The above inequality is clearly impossible and thus, the coordinates of the given point does not satisfy this inequality.

This implies that the given point is not a solution of this system.

Thus, we can see that the coordinates of the given point satisfies the inequalities of the third system only.

Then, the point is a solution of the system given by and .

Learn more about geometric solutions of system of linear inequalities here:

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where is the diagram? shown below where? ?

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