Question

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

(1 point)
Responses

a x + y = 2

-x + 2y = 16

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

b -5x = y - 3

3x - 8y = 24

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

c -4x + y = 6

-5x - y = 21

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

d -5x + y = -2

-3x + 6y = -12

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

For option a:
x + y = 2
Substituting x = 0 and y = -2:
0 + (-2) ≠ 2

-x + 2y = 16
Substituting x = 0 and y = -2:
0 + 2(-2) ≠ 16

Therefore, option a is not the correct system.

For option b:
-5x = y - 3
Substituting x = 0 and y = -2:
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5

3x - 8y = 24
Substituting x = 0 and y = -2:
3(0) - 8(-2) ≠ 24

Therefore, option b is not the correct system.

For option c:
-4x + y = 6
Substituting x = 0 and y = -2:
-4(0) + (-2) = 6
-2 = 6

-5x - y = 21
Substituting x = 0 and y = -2:
-5(0) - (-2) ≠ 21

Therefore, option c is not the correct system.

For option d:
-5x + y = -2
Substituting x = 0 and y = -2:
-5(0) + (-2) = -2
-2 = -2

-3x + 6y = -12
Substituting x = 0 and y = -2:
-3(0) + 6(-2) = -12
-12 = -12

Therefore, option d is the correct system.

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

Answer 2

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

To determine which system the point (0, -2) is a solution to, we can substitute the point's coordinates into each system and check if the equations are satisfied.

a) For the system:
x + y = 2
-x + 2y = 16

Substituting (0, -2) into the first equation:
0 + (-2) = 2
-2 ≠ 2

Since the first equation is not satisfied, the point (0, -2) is not a solution for system a.

b) For the system:
-5x = y - 3
3x - 8y = 24

Substituting (0, -2) into the first equation:
-5(0) = -2 - 3
0 ≠ -5

Since the first equation is not satisfied, the point (0, -2) is not a solution for system b.

c) For the system:
-4x + y = 6
-5x - y = 21

Substituting (0, -2) into the first equation:
-4(0) + (-2) = 6
-2 = 6

Since the first equation is satisfied, let's check the second equation:
-5(0) - (-2) = 21
2 ≠ 21

Since the second equation is not satisfied, the point (0, -2) is not a solution for system c.

d) For the system:
-5x + y = -2
-3x + 6y = -12

Substituting (0, -2) into the first equation:
-5(0) + (-2) = -2
-2 = -2

Since the first equation is satisfied, let's check the second equation:
-3(0) + 6(-2) = -12
-12 = -12

Both equations are satisfied, so the point (0, -2) is a solution for system d.

Therefore, the point (0, -2) is a solution to system d:
-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 need to substitute the values of x and y from the given point into each system and check if the equation holds true.

System a:
Substituting x = 0 and y = -2 into the equations:
a) x + y = 2 --> 0 + (-2) = 2 is false
b) -x + 2y = 16 --> -0 + 2(-2) = 16 is false

System b:
Substituting x = 0 and y = -2 into the equations:
a) -5x = y - 3 --> -5(0) = -2 - 3 is false
b) 3x - 8y = 24 --> 3(0) - 8(-2) = 24 is true

System c:
Substituting x = 0 and y = -2 into the equations:
a) -4x + y = 6 --> -4(0) + (-2) = 6 is false
b) -5x - y = 21 --> -5(0) - (-2) = 21 is false

System d:
Substituting x = 0 and y = -2 into the equations:
a) -5x + y = -2 --> -5(0) + (-2) = -2 is true
b) -3x + 6y = -12 --> -3(0) + 6(-2) = -12 is true

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