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Simplifying 5x + 3yi + 2y + -1xi = 3 + -1i Reorder the terms: -1ix + 3iy + 5x + 2y = 3 + -1i Solving -1ix + 3iy + 5x + 2y = 3 + -1i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i' to each side of the equation. -1ix + 3iy + 5x + i + 2y = 3 + -1i + i Reorder the terms: i + -1ix + 3iy + 5x + 2y = 3 + -1i + i Combine like terms: -1i + i = 0 i + -1ix + 3iy + 5x + 2y = 3 + 0 i + -1ix + 3iy + 5x + 2y = 3 Add '-5x' to each side of the equation. i + -1ix + 3iy + 5x + -5x + 2y = 3 + -5x Combine like terms: 5x + -5x = 0 i + -1ix + 3iy + 0 + 2y = 3 + -5x i + -1ix + 3iy + 2y = 3 + -5x Add '-2y' to each side of the equation. i + -1ix + 3iy + 2y + -2y = 3 + -5x + -2y Combine like terms: 2y + -2y = 0 i + -1ix + 3iy + 0 = 3 + -5x + -2y i + -1ix + 3iy = 3 + -5x + -2y Reorder the terms: -3 + i + -1ix + 3iy + 5x + 2y = 3 + -5x + -2y + -3 + 5x + 2y Reorder the terms: -3 + i + -1ix + 3iy + 5x + 2y = 3 + -3 + -5x + 5x + -2y + 2y Combine like terms: 3 + -3 = 0 -3 + i + -1ix + 3iy + 5x + 2y = 0 + -5x + 5x + -2y + 2y -3 + i + -1ix + 3iy + 5x + 2y = -5x + 5x + -2y + 2y Combine like terms: -5x + 5x = 0 -3 + i + -1ix + 3iy + 5x + 2y = 0 + -2y + 2y -3 + i + -1ix + 3iy + 5x + 2y = -2y + 2y Combine like terms: -2y + 2y = 0 -3 + i + -1ix + 3iy + 5x + 2y = 0 The solution to this equation could not be determined.
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