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Simplifying (4x2 + -1xy + y2) + (-1x2 + -5xy + 2y2) = 0 Reorder the terms: (-1xy + 4x2 + y2) + (-1x2 + -5xy + 2y2) = 0 Remove parenthesis around (-1xy + 4x2 + y2) -1xy + 4x2 + y2 + (-1x2 + -5xy + 2y2) = 0 Reorder the terms: -1xy + 4x2 + y2 + (-5xy + -1x2 + 2y2) = 0 Remove parenthesis around (-5xy + -1x2 + 2y2) -1xy + 4x2 + y2 + -5xy + -1x2 + 2y2 = 0 Reorder the terms: -1xy + -5xy + 4x2 + -1x2 + y2 + 2y2 = 0 Combine like terms: -1xy + -5xy = -6xy -6xy + 4x2 + -1x2 + y2 + 2y2 = 0 Combine like terms: 4x2 + -1x2 = 3x2 -6xy + 3x2 + y2 + 2y2 = 0 Combine like terms: y2 + 2y2 = 3y2 -6xy + 3x2 + 3y2 = 0 Solving -6xy + 3x2 + 3y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2xy + x2 + y2) = 0 Factor a trinomial. 3((x + -1y)(x + -1y)) = 0 Ignore the factor 3.Subproblem 1
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 = ySubproblem 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 = {y, y}
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