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Simplifying 24cz + -12cy + -6bz + 3by = 0 Reorder the terms: 3by + -6bz + -12cy + 24cz = 0 Solving 3by + -6bz + -12cy + 24cz = 0 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '12cy' to each side of the equation. 3by + -6bz + -12cy + 12cy + 24cz = 0 + 12cy Combine like terms: -12cy + 12cy = 0 3by + -6bz + 0 + 24cz = 0 + 12cy 3by + -6bz + 24cz = 0 + 12cy Remove the zero: 3by + -6bz + 24cz = 12cy Add '-24cz' to each side of the equation. 3by + -6bz + 24cz + -24cz = 12cy + -24cz Combine like terms: 24cz + -24cz = 0 3by + -6bz + 0 = 12cy + -24cz 3by + -6bz = 12cy + -24cz Reorder the terms: 3by + -6bz + -12cy + 24cz = 12cy + -12cy + -24cz + 24cz Combine like terms: 12cy + -12cy = 0 3by + -6bz + -12cy + 24cz = 0 + -24cz + 24cz 3by + -6bz + -12cy + 24cz = -24cz + 24cz Combine like terms: -24cz + 24cz = 0 3by + -6bz + -12cy + 24cz = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(by + -2bz + -4cy + 8cz) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(by + -2bz + -4cy + 8cz)' equal to zero and attempt to solve: Simplifying by + -2bz + -4cy + 8cz = 0 Solving by + -2bz + -4cy + 8cz = 0 Move all terms containing b to the left, all other terms to the right. Add '4cy' to each side of the equation. by + -2bz + -4cy + 4cy + 8cz = 0 + 4cy Combine like terms: -4cy + 4cy = 0 by + -2bz + 0 + 8cz = 0 + 4cy by + -2bz + 8cz = 0 + 4cy Remove the zero: by + -2bz + 8cz = 4cy Add '-8cz' to each side of the equation. by + -2bz + 8cz + -8cz = 4cy + -8cz Combine like terms: 8cz + -8cz = 0 by + -2bz + 0 = 4cy + -8cz by + -2bz = 4cy + -8cz 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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