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Simplifying (3x + -1y + 1) + -1(x + -1y) + (y + -1x) = 0 Reorder the terms: (1 + 3x + -1y) + -1(x + -1y) + (y + -1x) = 0 Remove parenthesis around (1 + 3x + -1y) 1 + 3x + -1y + -1(x + -1y) + (y + -1x) = 0 1 + 3x + -1y + (x * -1 + -1y * -1) + (y + -1x) = 0 1 + 3x + -1y + (-1x + 1y) + (y + -1x) = 0 Reorder the terms: 1 + 3x + -1y + -1x + 1y + (-1x + y) = 0 Remove parenthesis around (-1x + y) 1 + 3x + -1y + -1x + 1y + -1x + y = 0 Reorder the terms: 1 + 3x + -1x + -1x + -1y + 1y + y = 0 Combine like terms: 3x + -1x = 2x 1 + 2x + -1x + -1y + 1y + y = 0 Combine like terms: 2x + -1x = 1x 1 + 1x + -1y + 1y + y = 0 Combine like terms: -1y + 1y = 0 1 + 1x + 0 + y = 0 1 + 1x + y = 0 Solving 1 + 1x + y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 1x + -1 + y = 0 + -1 Reorder the terms: 1 + -1 + 1x + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1x + y = 0 + -1 1x + y = 0 + -1 Combine like terms: 0 + -1 = -1 1x + y = -1 Add '-1y' to each side of the equation. 1x + y + -1y = -1 + -1y Combine like terms: y + -1y = 0 1x + 0 = -1 + -1y 1x = -1 + -1y Divide each side by '1'. x = -1 + -1y Simplifying x = -1 + -1y
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