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