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Simplifying 32ax + 12bx + -14ay + -18by = 0 Reorder the terms: 32ax + -14ay + 12bx + -18by = 0 Solving 32ax + -14ay + 12bx + -18by = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-12bx' to each side of the equation. 32ax + -14ay + 12bx + -12bx + -18by = 0 + -12bx Combine like terms: 12bx + -12bx = 0 32ax + -14ay + 0 + -18by = 0 + -12bx 32ax + -14ay + -18by = 0 + -12bx Remove the zero: 32ax + -14ay + -18by = -12bx Add '18by' to each side of the equation. 32ax + -14ay + -18by + 18by = -12bx + 18by Combine like terms: -18by + 18by = 0 32ax + -14ay + 0 = -12bx + 18by 32ax + -14ay = -12bx + 18by Reorder the terms: 32ax + -14ay + 12bx + -18by = -12bx + 12bx + 18by + -18by Combine like terms: -12bx + 12bx = 0 32ax + -14ay + 12bx + -18by = 0 + 18by + -18by 32ax + -14ay + 12bx + -18by = 18by + -18by Combine like terms: 18by + -18by = 0 32ax + -14ay + 12bx + -18by = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(16ax + -7ay + 6bx + -9by) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16ax + -7ay + 6bx + -9by)' equal to zero and attempt to solve: Simplifying 16ax + -7ay + 6bx + -9by = 0 Solving 16ax + -7ay + 6bx + -9by = 0 Move all terms containing a to the left, all other terms to the right. Add '-6bx' to each side of the equation. 16ax + -7ay + 6bx + -6bx + -9by = 0 + -6bx Combine like terms: 6bx + -6bx = 0 16ax + -7ay + 0 + -9by = 0 + -6bx 16ax + -7ay + -9by = 0 + -6bx Remove the zero: 16ax + -7ay + -9by = -6bx Add '9by' to each side of the equation. 16ax + -7ay + -9by + 9by = -6bx + 9by Combine like terms: -9by + 9by = 0 16ax + -7ay + 0 = -6bx + 9by 16ax + -7ay = -6bx + 9by 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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