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Simplifying (4 + 3i) * x + (2 + -1i) * y = 6 + 7i Reorder the terms for easier multiplication: x(4 + 3i) + (2 + -1i) * y = 6 + 7i (4 * x + 3i * x) + (2 + -1i) * y = 6 + 7i Reorder the terms: (3ix + 4x) + (2 + -1i) * y = 6 + 7i (3ix + 4x) + (2 + -1i) * y = 6 + 7i Reorder the terms for easier multiplication: 3ix + 4x + y(2 + -1i) = 6 + 7i 3ix + 4x + (2 * y + -1i * y) = 6 + 7i Reorder the terms: 3ix + 4x + (-1iy + 2y) = 6 + 7i 3ix + 4x + (-1iy + 2y) = 6 + 7i Reorder the terms: 3ix + -1iy + 4x + 2y = 6 + 7i Solving 3ix + -1iy + 4x + 2y = 6 + 7i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-7i' to each side of the equation. 3ix + -1iy + 4x + -7i + 2y = 6 + 7i + -7i Reorder the terms: -7i + 3ix + -1iy + 4x + 2y = 6 + 7i + -7i Combine like terms: 7i + -7i = 0 -7i + 3ix + -1iy + 4x + 2y = 6 + 0 -7i + 3ix + -1iy + 4x + 2y = 6 Add '-4x' to each side of the equation. -7i + 3ix + -1iy + 4x + -4x + 2y = 6 + -4x Combine like terms: 4x + -4x = 0 -7i + 3ix + -1iy + 0 + 2y = 6 + -4x -7i + 3ix + -1iy + 2y = 6 + -4x Add '-2y' to each side of the equation. -7i + 3ix + -1iy + 2y + -2y = 6 + -4x + -2y Combine like terms: 2y + -2y = 0 -7i + 3ix + -1iy + 0 = 6 + -4x + -2y -7i + 3ix + -1iy = 6 + -4x + -2y Reorder the terms: -6 + -7i + 3ix + -1iy + 4x + 2y = 6 + -4x + -2y + -6 + 4x + 2y Reorder the terms: -6 + -7i + 3ix + -1iy + 4x + 2y = 6 + -6 + -4x + 4x + -2y + 2y Combine like terms: 6 + -6 = 0 -6 + -7i + 3ix + -1iy + 4x + 2y = 0 + -4x + 4x + -2y + 2y -6 + -7i + 3ix + -1iy + 4x + 2y = -4x + 4x + -2y + 2y Combine like terms: -4x + 4x = 0 -6 + -7i + 3ix + -1iy + 4x + 2y = 0 + -2y + 2y -6 + -7i + 3ix + -1iy + 4x + 2y = -2y + 2y Combine like terms: -2y + 2y = 0 -6 + -7i + 3ix + -1iy + 4x + 2y = 0 The solution to this equation could not be determined.
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