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