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Simplifying 4x2 + 9y2 = 13xy Solving 4x2 + 9y2 = 13xy Solving for variable 'x'. Reorder the terms: -13xy + 4x2 + 9y2 = 13xy + -13xy Combine like terms: 13xy + -13xy = 0 -13xy + 4x2 + 9y2 = 0 Factor a trinomial. (4x + -9y)(x + -1y) = 0Subproblem 1
Set the factor '(4x + -9y)' equal to zero and attempt to solve: Simplifying 4x + -9y = 0 Solving 4x + -9y = 0 Move all terms containing x to the left, all other terms to the right. Add '9y' to each side of the equation. 4x + -9y + 9y = 0 + 9y Combine like terms: -9y + 9y = 0 4x + 0 = 0 + 9y 4x = 0 + 9y Remove the zero: 4x = 9y Divide each side by '4'. x = 2.25y Simplifying x = 2.25ySubproblem 2
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. x + -1y + y = 0 + y Combine like terms: -1y + y = 0 x + 0 = 0 + y x = 0 + y Remove the zero: x = y Simplifying x = ySolution
x = {2.25y, y}
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