Mathematics, 03.08.2021 23:00 dlatricewilcoxp0tsdw

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

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Answer from: mairxaromo

The point (-2,2) is a solution of the system given by and $y \geq -x-3$

Given point: (-2,2)

Given systems:

and

and

and $y \geq -x-3$

and $y \geq -2x-5$

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) y-2x+2 and yx+5

Substitute the coordinates of the point (-2,2) into the inequalities of the system.

Put x=-2,y=2 in y-2x+2 to get,

2-2(-2)+2

24+2

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 yx-1

Substitute the coordinates of the point (-2,2) into the inequalities of the system.

Put x=-2,y=2 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 $y \geq -x-3$

Substitute the coordinates of the point (-2,2) into the inequalities of the system.

Put x=-2,y=2 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 x=-2,y=2 in $y \geq -x-3$ to get,

$2 \geq -(-2)-3$

$2 \geq 2-3$

$2 \geq -1$

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 $y \geq -2x-5$

Substitute the coordinates of the point (-2,2) into the inequalities of the system.

Put x=-2,y=2 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 (-2,2) satisfies the inequalities of the third system only.

Then, the point (-2,2) is a solution of the system given by and $y \geq -x-3$ .

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

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