Questlon 12 Rewrite the equation in \( A x+B y=C \) form Use integers for \( A, B \), and \( C \). \[ y+6=5(x+4) \]
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To rewrite the equation \( y + 6 = 5(x + 4) \) in the form \( Ax + By = C \), first simplify the right side. Distributing the 5 gives: \[ y + 6 = 5x + 20. \] Next, subtract 6 from both sides: \[ y = 5x + 14. \] Now, rearranging this into the standard form \( Ax + By = C \), we get: \[ -5x + y = 14. \] To express it with positive coefficients, we multiply through by -1: \[ 5x - y = -14. \] Thus, in the form \( Ax + By = C \), the integers are \( A = 5 \), \( B = -1 \), and \( C = -14 \).