To determine which student found the correct solution for the equation \(3x - 4y = 8\), we can substitute each student's proposed solution into the equation.
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Linda's solution \((1, -4)\): \[ 3(1) - 4(-4) = 3 - (-16) = 3 + 16 = 19 \quad \text{(not a solution)} \]
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Nathan's solution \((5, 3)\): \[ 3(5) - 4(3) = 15 - 12 = 3 \quad \text{(not a solution)} \]
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Gary's solution \((4, 1)\): \[ 3(4) - 4(1) = 12 - 4 = 8 \quad \text{(is a solution)} \]
Based on these calculations, the correct solution is from Student #3: Gary, who correctly identified \((4, 1)\) as a solution to the equation \(3x - 4y = 8\).
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