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Simplifying 3(x + y) + 9k(x + y) = 0 (x * 3 + y * 3) + 9k(x + y) = 0 (3x + 3y) + 9k(x + y) = 0 3x + 3y + (x * 9k + y * 9k) = 0 3x + 3y + (9kx + 9ky) = 0 Reorder the terms: 9kx + 9ky + 3x + 3y = 0 Solving 9kx + 9ky + 3x + 3y = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3x' to each side of the equation. 9kx + 9ky + 3x + -3x + 3y = 0 + -3x Combine like terms: 3x + -3x = 0 9kx + 9ky + 0 + 3y = 0 + -3x 9kx + 9ky + 3y = 0 + -3x Remove the zero: 9kx + 9ky + 3y = -3x Add '-3y' to each side of the equation. 9kx + 9ky + 3y + -3y = -3x + -3y Combine like terms: 3y + -3y = 0 9kx + 9ky + 0 = -3x + -3y 9kx + 9ky = -3x + -3y Reorder the terms: 9kx + 9ky + 3x + 3y = -3x + 3x + -3y + 3y Combine like terms: -3x + 3x = 0 9kx + 9ky + 3x + 3y = 0 + -3y + 3y 9kx + 9ky + 3x + 3y = -3y + 3y Combine like terms: -3y + 3y = 0 9kx + 9ky + 3x + 3y = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3kx + 3ky + x + y) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3kx + 3ky + x + y)' equal to zero and attempt to solve: Simplifying 3kx + 3ky + x + y = 0 Solving 3kx + 3ky + x + y = 0 Move all terms containing k to the left, all other terms to the right. Add '-1x' to each side of the equation. 3kx + 3ky + x + -1x + y = 0 + -1x Combine like terms: x + -1x = 0 3kx + 3ky + 0 + y = 0 + -1x 3kx + 3ky + y = 0 + -1x Remove the zero: 3kx + 3ky + y = -1x Add '-1y' to each side of the equation. 3kx + 3ky + y + -1y = -1x + -1y Combine like terms: y + -1y = 0 3kx + 3ky + 0 = -1x + -1y 3kx + 3ky = -1x + -1y 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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