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Simplifying 6x2 + 6y2 = 13xy Solving 6x2 + 6y2 = 13xy Solving for variable 'x'. Reorder the terms: -13xy + 6x2 + 6y2 = 13xy + -13xy Combine like terms: 13xy + -13xy = 0 -13xy + 6x2 + 6y2 = 0 Factor a trinomial. (2x + -3y)(3x + -2y) = 0Subproblem 1
Set the factor '(2x + -3y)' equal to zero and attempt to solve: Simplifying 2x + -3y = 0 Solving 2x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 2x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 2x + 0 = 0 + 3y 2x = 0 + 3y Remove the zero: 2x = 3y Divide each side by '2'. x = 1.5y Simplifying x = 1.5ySubproblem 2
Set the factor '(3x + -2y)' equal to zero and attempt to solve: Simplifying 3x + -2y = 0 Solving 3x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 3x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 3x + 0 = 0 + 2y 3x = 0 + 2y Remove the zero: 3x = 2y Divide each side by '3'. x = 0.6666666667y Simplifying x = 0.6666666667ySolution
x = {1.5y, 0.6666666667y}
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