To determine which system the point (0, -2) is a solution for, we need to substitute \(x = 0\) and \(y = -2\) into each equation in each given system.
Let's check each option:
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For the system:
- \(-5x + y = -2\)
- \(-3x + 6y = -12\)
Substituting \(x = 0\) and \(y = -2\):
- For \(-5(0) + (-2) = -2\) → \(-2 = -2\) (True)
- For \(-3(0) + 6(-2) = -12\) → \(0 - 12 = -12\) (True)
So, (0, -2) is a solution for this system.
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For the system:
- \(-4x + y = 6\)
- \(-5x - y = 21\)
Substituting:
- For \(-4(0) + (-2) = 6\) → \(-2 = 6\) (False)
Not a solution.
-
For the system:
- \(x + y = 2\)
- \(-x + 2y = 16\)
Substituting:
- For \(0 + (-2) = 2\) → \(-2 = 2\) (False)
Not a solution.
-
For the system:
- \(-5x = y - 3\)
- \(3x - 8y = 24\)
Substituting:
- For \(-5(0) = -2 - 3\) → \(0 = -5\) (False)
Not a solution.
Based on the checks, the point (0, -2) is a solution to the first system:
\(-5x + y = -2\) and \(-3x + 6y = -12\).