To determine which system of equations the point (0, -2) is a solution to, we substitute x = 0 and y = -2 into each equation of the systems provided.
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System:
- \( x + y = 2 \)
- \( -x + 2y = 16 \)
Substituting (0, -2):
- \( 0 + (-2) = 2 \) → \( -2 = 2 \) (not true)
- \( -0 + 2(-2) = 16 \) → \( -4 = 16 \) (not true)
This system does not work.
-
System:
- \( x + y = 2 \)
- \( -x + 2y = 16 \)
This is the same as above.
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System:
- \( -5x = y - 3 \)
- \( 3x - 8y = 24 \)
Substituting (0, -2):
- \( -5(0) = -2 - 3 \) → \( 0 = -5 \) (not true)
- \( 3(0) - 8(-2) = 24 \) → \( 0 + 16 = 24 \) (not true)
This system does not work.
-
System:
- \( -5x + y = -2 \)
- \( -3x + 6y = -12 \)
Substituting (0, -2):
- \( -5(0) - 2 = -2 \) → \( 0 - 2 = -2 \) (true)
- \( -3(0) + 6(-2) = -12 \) → \( 0 - 12 = -12 \) (true)
This system works!
-
System:
- \( -4x + y = 6 \)
- \( -5x - y = 21 \)
Substituting (0, -2):
- \( -4(0) - 2 = 6 \) → \( 0 - 2 = 6 \) (not true)
- \( -5(0) - (-2) = 21 \) → \( 0 + 2 = 21 \) (not true)
This system does not work.
Therefore, the point (0, -2) is a solution to the system: -5x + y = -2 and -3x + 6y = -12.