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