To determine which student found the correct solution to the equation \(3x - 4y = 8\), we will substitute the coordinates of each student's proposed solution into the equation.
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For Linda's solution \((1, -4)\):
\[ 3(1) - 4(-4) = 3 - (-16) = 3 + 16 = 19 \quad \text{(not equal to 8)} \]
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For Nathan's solution \((5, 3)\):
\[ 3(5) - 4(3) = 15 - 12 = 3 \quad \text{(not equal to 8)} \]
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For Gary's solution \((4, 1)\):
\[ 3(4) - 4(1) = 12 - 4 = 8 \quad \text{(equal to 8)} \]
From these calculations, only Gary's solution \((4, 1)\) satisfies the equation.
Therefore, Student #3 (Gary) is correct.
1 answer