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Simplifying a * x + b * y = c Multiply a * x ax + b * y = c Multiply b * y ax + by = c Solving ax + by = c 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 + -1by = -1by + c Combine like terms: by + -1by = 0 ax + 0 = -1by + c ax = -1by + c Divide each side by 'x'. a = -1bx-1y + cx-1 Simplifying a = -1bx-1y + cx-1
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