Question

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The point (0,-2) is a solution to which system?

(1 point)
Responses

x + y = 2

-x + 2y = 16

x + y = 2 -x + 2y = 16

-5x = y - 3

3x - 8y = 24

-5x = y - 3 3x - 8y = 24

-4x + y = 6

-5x - y = 21

-4x + y = 6 -5x - y = 21

-5x + y = -2

-3x + 6y = -12

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the system of equations that the point (0,-2) is a solution to, we can substitute the values x = 0 and y = -2 into each equation and see which equations are satisfied.

For the first equation, x + y = 2:
0 + (-2) = 2
-2 = 2
This equation is not satisfied by the point (0,-2).

For the second equation, -x + 2y = 16:
-(0) + 2(-2) = 16
-4 = 16
This equation is not satisfied by the point (0,-2).

For the third equation, x + y = 2 and -x + 2y = 16:
0 + (-2) = 2
-2 = 2
-(0) + 2(-2) = 16
-4 = 16
Both equations are not satisfied by the point (0,-2).

For the fourth equation, -5x = y - 3:
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5
This equation is not satisfied by the point (0,-2).

For the fifth equation, 3x - 8y = 24:
3(0) - 8(-2) = 24
16 = 24
This equation is not satisfied by the point (0,-2).

For the sixth equation, -5x = y - 3 and 3x - 8y = 24:
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5
3(0) - 8(-2) = 24
16 = 24
Both equations are not satisfied by the point (0,-2).

For the seventh equation, -4x + y = 6:
-4(0) + (-2) = 6
-2 = 6
This equation is not satisfied by the point (0,-2).

For the eighth equation, -5x - y = 21:
-5(0) - (-2) = 21
2 = 21
This equation is not satisfied by the point (0,-2).

For the ninth equation, -4x + y = 6 and -5x - y = 21:
-4(0) + (-2) = 6
-2 = 6
-5(0) - (-2) = 21
2 = 21
Both equations are not satisfied by the point (0,-2).

For the tenth equation, -5x + y = -2:
-5(0) + (-2) = -2
-2 = -2
This equation is satisfied by the point (0,-2).

For the eleventh equation, -3x + 6y = -12:
-3(0) + 6(-2) = -12
-12 = -12
This equation is satisfied by the point (0,-2).

Therefore, the point (0,-2) is a solution to the system of equations:
-5x + y = -2
-3x + 6y = -12

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine which system contains the point (0, -2) as a solution, we can substitute the x and y values of the point into each system of equations and see if they both evaluate correctly.

Let's go through each system:

System 1:
x + y = 2 - Equation 1
-x + 2y = 16 - Equation 2

Substituting x = 0 and y = -2 into Equation 1:
0 + (-2) = 2
-2 = 2

The left side and right side of Equation 1 do not match, so the point (0, -2) is not a solution to System 1.

System 2:
-5x = y - 3 - Equation 1
3x - 8y = 24 - Equation 2

Substituting x = 0 and y = -2 into Equation 1:
-5(0) = -2 - 3
0 = -5

The left side and right side of Equation 1 do not match, so the point (0, -2) is not a solution to System 2.

System 3:
-4x + y = 6 - Equation 1
-5x - y = 21 - Equation 2

Substituting x = 0 and y = -2 into Equation 1:
-4(0) + (-2) = 6
-2 = 6

The left side and right side of Equation 1 do not match, so the point (0, -2) is not a solution to System 3.

System 4:
-5x + y = -2 - Equation 1
-3x + 6y = -12 - Equation 2

Substituting x = 0 and y = -2 into Equation 1:
-5(0) + (-2) = -2
-2 = -2

The left side and right side of Equation 1 match, so the point (0, -2) is a solution to System 4.

Therefore, the point (0, -2) is a solution to the system:

-5x + y = -2
-3x + 6y = -12

Answer 3

[AI-generated answer — Explain Bot]

To determine which system the point (0,-2) is a solution to, we can substitute the values of x=0 and y=-2 into each equation and see which equations are satisfied.

For the first system:
x + y = 2
Substituting x=0 and y=-2:
0 + (-2) = 2
-2 = 2
This equation is not true, so (0,-2) is not a solution to the first system.

For the second system:
-x + 2y = 16
Substituting x=0 and y=-2:
-0 + 2(-2) = 16
-4 = 16
This equation is not true, so (0,-2) is not a solution to the second system.

For the third system:
x + y = 2
Substituting x=0 and y=-2:
0 + (-2) = 2
-2 = 2
This equation is not true, so (0,-2) is not a solution to the third system.

For the fourth system:
-5x = y - 3
Substituting x=0 and y=-2:
-5(0) = (-2) - 3
0 = -5
This equation is not true, so (0,-2) is not a solution to the fourth system.

For the fifth system:
3x - 8y = 24
Substituting x=0 and y=-2:
3(0) - 8(-2) = 24
16 = 24
This equation is not true, so (0,-2) is not a solution to the fifth system.

For the sixth system:
-4x + y = 6
Substituting x=0 and y=-2:
-4(0) + (-2) = 6
-2 = 6
This equation is not true, so (0,-2) is not a solution to the sixth system.

For the seventh system:
-5x - y = 21
Substituting x=0 and y=-2:
-5(0) - (-2) = 21
2 = 21
This equation is not true, so (0,-2) is not a solution to the seventh system.

For the eighth system:
-5x + y = -2
Substituting x=0 and y=-2:
-5(0) + (-2) = -2
-2 = -2
This equation is true, so (0,-2) is a solution to the eighth system.

For the ninth system:
-3x + 6y = -12
Substituting x=0 and y=-2:
-3(0) + 6(-2) = -12
-12 = -12
This equation is true, so (0,-2) is a solution to the ninth system.

Therefore, the point (0,-2) is a solution to the system represented by the eighth and ninth equations: -5x + y = -2 and -3x + 6y = -12.