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Simplifying -2x2 + 3y2 = 5xy Solving -2x2 + 3y2 = 5xy Solving for variable 'x'. Reorder the terms: -5xy + -2x2 + 3y2 = 5xy + -5xy Combine like terms: 5xy + -5xy = 0 -5xy + -2x2 + 3y2 = 0 Factor a trinomial. (-1x + -3y)(2x + -1y) = 0Subproblem 1
Set the factor '(-1x + -3y)' equal to zero and attempt to solve: Simplifying -1x + -3y = 0 Solving -1x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. -1x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 -1x + 0 = 0 + 3y -1x = 0 + 3y Remove the zero: -1x = 3y Divide each side by '-1'. x = -3y Simplifying x = -3ySubproblem 2
Set the factor '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 2x + -1y + y = 0 + y Combine like terms: -1y + y = 0 2x + 0 = 0 + y 2x = 0 + y Remove the zero: 2x = y Divide each side by '2'. x = 0.5y Simplifying x = 0.5ySolution
x = {-3y, 0.5y}
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