To determine which of the ordered pairs is a solution to the equation \(3x - 8 = -4y\), we can substitute each pair \((x, y)\) into the equation and check if it holds true.
Let's evaluate each option:
A. \((-1, 1)\) \[ x = -1, \quad y = 1 \] Substituting into the equation: \[ 3(-1) - 8 = -4(1) \] \[ -3 - 8 = -4 \] \[ -11 \neq -4 \] Not a solution.
B. \((0, -2)\) \[ x = 0, \quad y = -2 \] Substituting into the equation: \[ 3(0) - 8 = -4(-2) \] \[ -8 = 8 \] Not a solution.
C. \((0, 2)\) \[ x = 0, \quad y = 2 \] Substituting into the equation: \[ 3(0) - 8 = -4(2) \] \[ -8 = -8 \] This is a solution.
D. \((1, 1)\) \[ x = 1, \quad y = 1 \] Substituting into the equation: \[ 3(1) - 8 = -4(1) \] \[ 3 - 8 = -4 \] \[ -5 \neq -4 \] Not a solution.
The only ordered pair that is a solution to the equation \(3x - 8 = -4y\) is: C. \((0, 2)\).
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