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Simplifying (a + -1) * x + (b + -1) * y = 0 Reorder the terms: (-1 + a) * x + (b + -1) * y = 0 Reorder the terms for easier multiplication: x(-1 + a) + (b + -1) * y = 0 (-1 * x + a * x) + (b + -1) * y = 0 Reorder the terms: (ax + -1x) + (b + -1) * y = 0 (ax + -1x) + (b + -1) * y = 0 Reorder the terms: ax + -1x + (-1 + b) * y = 0 Reorder the terms for easier multiplication: ax + -1x + y(-1 + b) = 0 ax + -1x + (-1 * y + b * y) = 0 Reorder the terms: ax + -1x + (by + -1y) = 0 ax + -1x + (by + -1y) = 0 Reorder the terms: ax + by + -1x + -1y = 0 Solving ax + by + -1x + -1y = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1by' to each side of the equation. ax + by + -1x + -1by + -1y = 0 + -1by Reorder the terms: ax + by + -1by + -1x + -1y = 0 + -1by Combine like terms: by + -1by = 0 ax + 0 + -1x + -1y = 0 + -1by ax + -1x + -1y = 0 + -1by Remove the zero: ax + -1x + -1y = -1by Add 'x' to each side of the equation. ax + -1x + x + -1y = -1by + x Combine like terms: -1x + x = 0 ax + 0 + -1y = -1by + x ax + -1y = -1by + x Add 'y' to each side of the equation. ax + -1y + y = -1by + x + y Combine like terms: -1y + y = 0 ax + 0 = -1by + x + y ax = -1by + x + y Divide each side by 'x'. a = -1bx-1y + 1 + x-1y Simplifying a = -1bx-1y + 1 + x-1y Reorder the terms: a = 1 + -1bx-1y + x-1y
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