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Simplifying y(x) = 2x2 + -6x Multiply y * x xy = 2x2 + -6x Reorder the terms: xy = -6x + 2x2 Solving xy = -6x + 2x2 Solving for variable 'x'. Reorder the terms: 6x + xy + -2x2 = -6x + 2x2 + 6x + -2x2 Reorder the terms: 6x + xy + -2x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 6x + xy + -2x2 = 0 + 2x2 + -2x2 6x + xy + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 6x + xy + -2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(6 + y + -2x) = 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 '(6 + y + -2x)' equal to zero and attempt to solve: Simplifying 6 + y + -2x = 0 Reorder the terms: 6 + -2x + y = 0 Solving 6 + -2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -2x + -6 + y = 0 + -6 Reorder the terms: 6 + -6 + -2x + y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -2x + y = 0 + -6 -2x + y = 0 + -6 Combine like terms: 0 + -6 = -6 -2x + y = -6 Add '-1y' to each side of the equation. -2x + y + -1y = -6 + -1y Combine like terms: y + -1y = 0 -2x + 0 = -6 + -1y -2x = -6 + -1y Divide each side by '-2'. x = 3 + 0.5y Simplifying x = 3 + 0.5ySolution
x = {0, 3 + 0.5y}
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