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