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Simplifying 4xy + 2x + 2y + 2z = 280 * 4 Reorder the terms: 2x + 4xy + 2y + 2z = 280 * 4 Multiply 280 * 4 2x + 4xy + 2y + 2z = 1120 Solving 2x + 4xy + 2y + 2z = 1120 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 2x + 4xy + 2y + -2y + 2z = 1120 + -2y Combine like terms: 2y + -2y = 0 2x + 4xy + 0 + 2z = 1120 + -2y 2x + 4xy + 2z = 1120 + -2y Add '-2z' to each side of the equation. 2x + 4xy + 2z + -2z = 1120 + -2y + -2z Combine like terms: 2z + -2z = 0 2x + 4xy + 0 = 1120 + -2y + -2z 2x + 4xy = 1120 + -2y + -2z Reorder the terms: -1120 + 2x + 4xy + 2y + 2z = 1120 + -2y + -2z + -1120 + 2y + 2z Reorder the terms: -1120 + 2x + 4xy + 2y + 2z = 1120 + -1120 + -2y + 2y + -2z + 2z Combine like terms: 1120 + -1120 = 0 -1120 + 2x + 4xy + 2y + 2z = 0 + -2y + 2y + -2z + 2z -1120 + 2x + 4xy + 2y + 2z = -2y + 2y + -2z + 2z Combine like terms: -2y + 2y = 0 -1120 + 2x + 4xy + 2y + 2z = 0 + -2z + 2z -1120 + 2x + 4xy + 2y + 2z = -2z + 2z Combine like terms: -2z + 2z = 0 -1120 + 2x + 4xy + 2y + 2z = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-560 + x + 2xy + y + z) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-560 + x + 2xy + y + z)' equal to zero and attempt to solve: Simplifying -560 + x + 2xy + y + z = 0 Solving -560 + x + 2xy + y + z = 0 Move all terms containing x to the left, all other terms to the right. Add '560' to each side of the equation. -560 + x + 2xy + y + 560 + z = 0 + 560 Reorder the terms: -560 + 560 + x + 2xy + y + z = 0 + 560 Combine like terms: -560 + 560 = 0 0 + x + 2xy + y + z = 0 + 560 x + 2xy + y + z = 0 + 560 Combine like terms: 0 + 560 = 560 x + 2xy + y + z = 560 Add '-1y' to each side of the equation. x + 2xy + y + -1y + z = 560 + -1y Combine like terms: y + -1y = 0 x + 2xy + 0 + z = 560 + -1y x + 2xy + z = 560 + -1y Add '-1z' to each side of the equation. x + 2xy + z + -1z = 560 + -1y + -1z Combine like terms: z + -1z = 0 x + 2xy + 0 = 560 + -1y + -1z x + 2xy = 560 + -1y + -1z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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