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Simplifying -8x2 + 4y2 = -31xy Solving -8x2 + 4y2 = -31xy Solving for variable 'x'. Reorder the terms: 31xy + -8x2 + 4y2 = -31xy + 31xy Combine like terms: -31xy + 31xy = 0 31xy + -8x2 + 4y2 = 0 Factor a trinomial. (-8x + -1y)(x + -4y) = 0Subproblem 1
Set the factor '(-8x + -1y)' equal to zero and attempt to solve: Simplifying -8x + -1y = 0 Solving -8x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. -8x + -1y + y = 0 + y Combine like terms: -1y + y = 0 -8x + 0 = 0 + y -8x = 0 + y Remove the zero: -8x = y Divide each side by '-8'. x = -0.125y Simplifying x = -0.125ySubproblem 2
Set the factor '(x + -4y)' equal to zero and attempt to solve: Simplifying x + -4y = 0 Solving x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 x + 0 = 0 + 4y x = 0 + 4y Remove the zero: x = 4y Simplifying x = 4ySolution
x = {-0.125y, 4y}
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