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Simplifying 10x2 + 9y2 = 19xy Solving 10x2 + 9y2 = 19xy Solving for variable 'x'. Reorder the terms: -19xy + 10x2 + 9y2 = 19xy + -19xy Combine like terms: 19xy + -19xy = 0 -19xy + 10x2 + 9y2 = 0 Factor a trinomial. (x + -1y)(10x + -9y) = 0Subproblem 1
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 = ySubproblem 2
Set the factor '(10x + -9y)' equal to zero and attempt to solve: Simplifying 10x + -9y = 0 Solving 10x + -9y = 0 Move all terms containing x to the left, all other terms to the right. Add '9y' to each side of the equation. 10x + -9y + 9y = 0 + 9y Combine like terms: -9y + 9y = 0 10x + 0 = 0 + 9y 10x = 0 + 9y Remove the zero: 10x = 9y Divide each side by '10'. x = 0.9y Simplifying x = 0.9ySolution
x = {y, 0.9y}
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