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Simplifying 30ax + -15ay + 42x + -21y = 0 Solving 30ax + -15ay + 42x + -21y = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-42x' to each side of the equation. 30ax + -15ay + 42x + -42x + -21y = 0 + -42x Combine like terms: 42x + -42x = 0 30ax + -15ay + 0 + -21y = 0 + -42x 30ax + -15ay + -21y = 0 + -42x Remove the zero: 30ax + -15ay + -21y = -42x Add '21y' to each side of the equation. 30ax + -15ay + -21y + 21y = -42x + 21y Combine like terms: -21y + 21y = 0 30ax + -15ay + 0 = -42x + 21y 30ax + -15ay = -42x + 21y Reorder the terms: 30ax + -15ay + 42x + -21y = -42x + 42x + 21y + -21y Combine like terms: -42x + 42x = 0 30ax + -15ay + 42x + -21y = 0 + 21y + -21y 30ax + -15ay + 42x + -21y = 21y + -21y Combine like terms: 21y + -21y = 0 30ax + -15ay + 42x + -21y = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(10ax + -5ay + 14x + -7y) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10ax + -5ay + 14x + -7y)' equal to zero and attempt to solve: Simplifying 10ax + -5ay + 14x + -7y = 0 Solving 10ax + -5ay + 14x + -7y = 0 Move all terms containing a to the left, all other terms to the right. Add '-14x' to each side of the equation. 10ax + -5ay + 14x + -14x + -7y = 0 + -14x Combine like terms: 14x + -14x = 0 10ax + -5ay + 0 + -7y = 0 + -14x 10ax + -5ay + -7y = 0 + -14x Remove the zero: 10ax + -5ay + -7y = -14x Add '7y' to each side of the equation. 10ax + -5ay + -7y + 7y = -14x + 7y Combine like terms: -7y + 7y = 0 10ax + -5ay + 0 = -14x + 7y 10ax + -5ay = -14x + 7y 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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