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Simplifying (2 + -5i) * x + (1 + 3i) * y + -8 + 9i = 0 Reorder the terms for easier multiplication: x(2 + -5i) + (1 + 3i) * y + -8 + 9i = 0 (2 * x + -5i * x) + (1 + 3i) * y + -8 + 9i = 0 Reorder the terms: (-5ix + 2x) + (1 + 3i) * y + -8 + 9i = 0 (-5ix + 2x) + (1 + 3i) * y + -8 + 9i = 0 Reorder the terms for easier multiplication: -5ix + 2x + y(1 + 3i) + -8 + 9i = 0 -5ix + 2x + (1 * y + 3i * y) + -8 + 9i = 0 Reorder the terms: -5ix + 2x + (3iy + 1y) + -8 + 9i = 0 -5ix + 2x + (3iy + 1y) + -8 + 9i = 0 Reorder the terms: -8 + 9i + -5ix + 3iy + 2x + 1y = 0 Solving -8 + 9i + -5ix + 3iy + 2x + 1y = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 9i + -5ix + 3iy + 2x + 8 + 1y = 0 + 8 Reorder the terms: -8 + 8 + 9i + -5ix + 3iy + 2x + 1y = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 9i + -5ix + 3iy + 2x + 1y = 0 + 8 9i + -5ix + 3iy + 2x + 1y = 0 + 8 Combine like terms: 0 + 8 = 8 9i + -5ix + 3iy + 2x + 1y = 8 Add '-2x' to each side of the equation. 9i + -5ix + 3iy + 2x + -2x + 1y = 8 + -2x Combine like terms: 2x + -2x = 0 9i + -5ix + 3iy + 0 + 1y = 8 + -2x 9i + -5ix + 3iy + 1y = 8 + -2x Add '-1y' to each side of the equation. 9i + -5ix + 3iy + 1y + -1y = 8 + -2x + -1y Combine like terms: 1y + -1y = 0 9i + -5ix + 3iy + 0 = 8 + -2x + -1y 9i + -5ix + 3iy = 8 + -2x + -1y Reorder the terms: -8 + 9i + -5ix + 3iy + 2x + y = 8 + -2x + -1y + -8 + 2x + y Reorder the terms: -8 + 9i + -5ix + 3iy + 2x + y = 8 + -8 + -2x + 2x + -1y + y Combine like terms: 8 + -8 = 0 -8 + 9i + -5ix + 3iy + 2x + y = 0 + -2x + 2x + -1y + y -8 + 9i + -5ix + 3iy + 2x + y = -2x + 2x + -1y + y Combine like terms: -2x + 2x = 0 -8 + 9i + -5ix + 3iy + 2x + y = 0 + -1y + y -8 + 9i + -5ix + 3iy + 2x + y = -1y + y Combine like terms: -1y + y = 0 -8 + 9i + -5ix + 3iy + 2x + y = 0 The solution to this equation could not be determined.
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