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