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Simplifying 0 = (x + y)(a + -1b) + (x + y)(2a + -1b) Multiply (x + y) * (a + -1b) 0 = (x(a + -1b) + y(a + -1b)) + (x + y)(2a + -1b) 0 = ((a * x + -1b * x) + y(a + -1b)) + (x + y)(2a + -1b) 0 = ((ax + -1bx) + y(a + -1b)) + (x + y)(2a + -1b) 0 = (ax + -1bx + (a * y + -1b * y)) + (x + y)(2a + -1b) 0 = (ax + -1bx + (ay + -1by)) + (x + y)(2a + -1b) Reorder the terms: 0 = (ax + ay + -1bx + -1by) + (x + y)(2a + -1b) 0 = (ax + ay + -1bx + -1by) + (x + y)(2a + -1b) Multiply (x + y) * (2a + -1b) 0 = ax + ay + -1bx + -1by + (x(2a + -1b) + y(2a + -1b)) 0 = ax + ay + -1bx + -1by + ((2a * x + -1b * x) + y(2a + -1b)) 0 = ax + ay + -1bx + -1by + ((2ax + -1bx) + y(2a + -1b)) 0 = ax + ay + -1bx + -1by + (2ax + -1bx + (2a * y + -1b * y)) 0 = ax + ay + -1bx + -1by + (2ax + -1bx + (2ay + -1by)) Reorder the terms: 0 = ax + ay + -1bx + -1by + (2ax + 2ay + -1bx + -1by) 0 = ax + ay + -1bx + -1by + (2ax + 2ay + -1bx + -1by) Reorder the terms: 0 = ax + 2ax + ay + 2ay + -1bx + -1bx + -1by + -1by Combine like terms: ax + 2ax = 3ax 0 = 3ax + ay + 2ay + -1bx + -1bx + -1by + -1by Combine like terms: ay + 2ay = 3ay 0 = 3ax + 3ay + -1bx + -1bx + -1by + -1by Combine like terms: -1bx + -1bx = -2bx 0 = 3ax + 3ay + -2bx + -1by + -1by Combine like terms: -1by + -1by = -2by 0 = 3ax + 3ay + -2bx + -2by Solving 0 = 3ax + 3ay + -2bx + -2by Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3ax' to each side of the equation. 0 + -3ax = 3ax + 3ay + -2bx + -3ax + -2by Remove the zero: -3ax = 3ax + 3ay + -2bx + -3ax + -2by Reorder the terms: -3ax = 3ax + -3ax + 3ay + -2bx + -2by Combine like terms: 3ax + -3ax = 0 -3ax = 0 + 3ay + -2bx + -2by -3ax = 3ay + -2bx + -2by Add '-3ay' to each side of the equation. -3ax + -3ay = 3ay + -2bx + -3ay + -2by Reorder the terms: -3ax + -3ay = 3ay + -3ay + -2bx + -2by Combine like terms: 3ay + -3ay = 0 -3ax + -3ay = 0 + -2bx + -2by -3ax + -3ay = -2bx + -2by Reorder the terms: -3ax + -3ay + 2bx + 2by = -2bx + 2bx + -2by + 2by Combine like terms: -2bx + 2bx = 0 -3ax + -3ay + 2bx + 2by = 0 + -2by + 2by -3ax + -3ay + 2bx + 2by = -2by + 2by Combine like terms: -2by + 2by = 0 -3ax + -3ay + 2bx + 2by = 0 The solution to this equation could not be determined.
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