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Simplifying (5 + 3i) * x + -1(2 + 3i) * y = 4 + -6i Reorder the terms for easier multiplication: x(5 + 3i) + -1(2 + 3i) * y = 4 + -6i (5 * x + 3i * x) + -1(2 + 3i) * y = 4 + -6i Reorder the terms: (3ix + 5x) + -1(2 + 3i) * y = 4 + -6i (3ix + 5x) + -1(2 + 3i) * y = 4 + -6i Reorder the terms for easier multiplication: 3ix + 5x + -1y(2 + 3i) = 4 + -6i 3ix + 5x + (2 * -1y + 3i * -1y) = 4 + -6i Reorder the terms: 3ix + 5x + (-3iy + -2y) = 4 + -6i 3ix + 5x + (-3iy + -2y) = 4 + -6i Reorder the terms: 3ix + -3iy + 5x + -2y = 4 + -6i Solving 3ix + -3iy + 5x + -2y = 4 + -6i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '6i' to each side of the equation. 3ix + -3iy + 5x + 6i + -2y = 4 + -6i + 6i Reorder the terms: 6i + 3ix + -3iy + 5x + -2y = 4 + -6i + 6i Combine like terms: -6i + 6i = 0 6i + 3ix + -3iy + 5x + -2y = 4 + 0 6i + 3ix + -3iy + 5x + -2y = 4 Add '-5x' to each side of the equation. 6i + 3ix + -3iy + 5x + -5x + -2y = 4 + -5x Combine like terms: 5x + -5x = 0 6i + 3ix + -3iy + 0 + -2y = 4 + -5x 6i + 3ix + -3iy + -2y = 4 + -5x Add '2y' to each side of the equation. 6i + 3ix + -3iy + -2y + 2y = 4 + -5x + 2y Combine like terms: -2y + 2y = 0 6i + 3ix + -3iy + 0 = 4 + -5x + 2y 6i + 3ix + -3iy = 4 + -5x + 2y Reorder the terms: -4 + 6i + 3ix + -3iy + 5x + -2y = 4 + -5x + 2y + -4 + 5x + -2y Reorder the terms: -4 + 6i + 3ix + -3iy + 5x + -2y = 4 + -4 + -5x + 5x + 2y + -2y Combine like terms: 4 + -4 = 0 -4 + 6i + 3ix + -3iy + 5x + -2y = 0 + -5x + 5x + 2y + -2y -4 + 6i + 3ix + -3iy + 5x + -2y = -5x + 5x + 2y + -2y Combine like terms: -5x + 5x = 0 -4 + 6i + 3ix + -3iy + 5x + -2y = 0 + 2y + -2y -4 + 6i + 3ix + -3iy + 5x + -2y = 2y + -2y Combine like terms: 2y + -2y = 0 -4 + 6i + 3ix + -3iy + 5x + -2y = 0 The solution to this equation could not be determined.
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