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Simplifying (x + -1y)(3x + -4y) = 0 Multiply (x + -1y) * (3x + -4y) (x(3x + -4y) + -1y * (3x + -4y)) = 0 ((3x * x + -4y * x) + -1y * (3x + -4y)) = 0 Reorder the terms: ((-4xy + 3x2) + -1y * (3x + -4y)) = 0 ((-4xy + 3x2) + -1y * (3x + -4y)) = 0 (-4xy + 3x2 + (3x * -1y + -4y * -1y)) = 0 (-4xy + 3x2 + (-3xy + 4y2)) = 0 Reorder the terms: (-4xy + -3xy + 3x2 + 4y2) = 0 Combine like terms: -4xy + -3xy = -7xy (-7xy + 3x2 + 4y2) = 0 Solving -7xy + 3x2 + 4y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -4y)(x + -1y) = 0Subproblem 1
Set the factor '(3x + -4y)' equal to zero and attempt to solve: Simplifying 3x + -4y = 0 Solving 3x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. 3x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 3x + 0 = 0 + 4y 3x = 0 + 4y Remove the zero: 3x = 4y Divide each side by '3'. x = 1.333333333y Simplifying x = 1.333333333ySubproblem 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 = {1.333333333y, y}
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