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Simplifying xp + yp = zp Solving px + py = pz Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1pz' to each side of the equation. px + py + -1pz = pz + -1pz Combine like terms: pz + -1pz = 0 px + py + -1pz = 0 Factor out the Greatest Common Factor (GCF), 'p'. p(x + y + -1z) = 0Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(x + y + -1z)' equal to zero and attempt to solve: Simplifying x + y + -1z = 0 Solving x + y + -1z = 0 Move all terms containing p to the left, all other terms to the right. Add '-1x' to each side of the equation. x + y + -1x + -1z = 0 + -1x Reorder the terms: x + -1x + y + -1z = 0 + -1x Combine like terms: x + -1x = 0 0 + y + -1z = 0 + -1x y + -1z = 0 + -1x Remove the zero: y + -1z = -1x Add '-1y' to each side of the equation. y + -1y + -1z = -1x + -1y Combine like terms: y + -1y = 0 0 + -1z = -1x + -1y -1z = -1x + -1y Add 'z' to each side of the equation. -1z + z = -1x + -1y + z Combine like terms: -1z + z = 0 0 = -1x + -1y + z Simplifying 0 = -1x + -1y + z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
p = {0}
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