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Simplifying (3x + -2y) + -1(x + -7y) * i = 1 + -1(y + -4) * i Remove parenthesis around (3x + -2y) 3x + -2y + -1(x + -7y) * i = 1 + -1(y + -4) * i Reorder the terms for easier multiplication: 3x + -2y + -1i(x + -7y) = 1 + -1(y + -4) * i 3x + -2y + (x * -1i + -7y * -1i) = 1 + -1(y + -4) * i 3x + -2y + (-1ix + 7iy) = 1 + -1(y + -4) * i Reorder the terms: -1ix + 7iy + 3x + -2y = 1 + -1(y + -4) * i Reorder the terms: -1ix + 7iy + 3x + -2y = 1 + -1(-4 + y) * i Reorder the terms for easier multiplication: -1ix + 7iy + 3x + -2y = 1 + -1i(-4 + y) -1ix + 7iy + 3x + -2y = 1 + (-4 * -1i + y * -1i) -1ix + 7iy + 3x + -2y = 1 + (4i + -1iy) Solving -1ix + 7iy + 3x + -2y = 1 + 4i + -1iy Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4i' to each side of the equation. -1ix + 7iy + 3x + -4i + -2y = 1 + 4i + -4i + -1iy Reorder the terms: -4i + -1ix + 7iy + 3x + -2y = 1 + 4i + -4i + -1iy Combine like terms: 4i + -4i = 0 -4i + -1ix + 7iy + 3x + -2y = 1 + 0 + -1iy -4i + -1ix + 7iy + 3x + -2y = 1 + -1iy Add 'iy' to each side of the equation. -4i + -1ix + 7iy + 3x + iy + -2y = 1 + -1iy + iy Reorder the terms: -4i + -1ix + 7iy + iy + 3x + -2y = 1 + -1iy + iy Combine like terms: 7iy + iy = 8iy -4i + -1ix + 8iy + 3x + -2y = 1 + -1iy + iy Combine like terms: -1iy + iy = 0 -4i + -1ix + 8iy + 3x + -2y = 1 + 0 -4i + -1ix + 8iy + 3x + -2y = 1 Add '-3x' to each side of the equation. -4i + -1ix + 8iy + 3x + -3x + -2y = 1 + -3x Combine like terms: 3x + -3x = 0 -4i + -1ix + 8iy + 0 + -2y = 1 + -3x -4i + -1ix + 8iy + -2y = 1 + -3x Add '2y' to each side of the equation. -4i + -1ix + 8iy + -2y + 2y = 1 + -3x + 2y Combine like terms: -2y + 2y = 0 -4i + -1ix + 8iy + 0 = 1 + -3x + 2y -4i + -1ix + 8iy = 1 + -3x + 2y Reorder the terms: -1 + -4i + -1ix + 8iy + 3x + -2y = 1 + -3x + 2y + -1 + 3x + -2y Reorder the terms: -1 + -4i + -1ix + 8iy + 3x + -2y = 1 + -1 + -3x + 3x + 2y + -2y Combine like terms: 1 + -1 = 0 -1 + -4i + -1ix + 8iy + 3x + -2y = 0 + -3x + 3x + 2y + -2y -1 + -4i + -1ix + 8iy + 3x + -2y = -3x + 3x + 2y + -2y Combine like terms: -3x + 3x = 0 -1 + -4i + -1ix + 8iy + 3x + -2y = 0 + 2y + -2y -1 + -4i + -1ix + 8iy + 3x + -2y = 2y + -2y Combine like terms: 2y + -2y = 0 -1 + -4i + -1ix + 8iy + 3x + -2y = 0 The solution to this equation could not be determined.
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