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Simplifying 3(3y + -1xi) + -2(2x + -3yi) = (5 + -10I) + -1(2x + -3yi) Reorder the terms: 3(-1ix + 3y) + -2(2x + -3yi) = (5 + -10I) + -1(2x + -3yi) (-1ix * 3 + 3y * 3) + -2(2x + -3yi) = (5 + -10I) + -1(2x + -3yi) (-3ix + 9y) + -2(2x + -3yi) = (5 + -10I) + -1(2x + -3yi) Reorder the terms: -3ix + 9y + -2(-3iy + 2x) = (5 + -10I) + -1(2x + -3yi) -3ix + 9y + (-3iy * -2 + 2x * -2) = (5 + -10I) + -1(2x + -3yi) -3ix + 9y + (6iy + -4x) = (5 + -10I) + -1(2x + -3yi) Reorder the terms: -3ix + 6iy + -4x + 9y = (5 + -10I) + -1(2x + -3yi) Remove parenthesis around (5 + -10I) -3ix + 6iy + -4x + 9y = 5 + -10I + -1(2x + -3yi) Reorder the terms: -3ix + 6iy + -4x + 9y = 5 + -10I + -1(-3iy + 2x) -3ix + 6iy + -4x + 9y = 5 + -10I + (-3iy * -1 + 2x * -1) -3ix + 6iy + -4x + 9y = 5 + -10I + (3iy + -2x) Solving -3ix + 6iy + -4x + 9y = 5 + -10I + 3iy + -2x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3iy' to each side of the equation. -3ix + 6iy + -4x + -3iy + 9y = 5 + -10I + 3iy + -3iy + -2x Reorder the terms: -3ix + 6iy + -3iy + -4x + 9y = 5 + -10I + 3iy + -3iy + -2x Combine like terms: 6iy + -3iy = 3iy -3ix + 3iy + -4x + 9y = 5 + -10I + 3iy + -3iy + -2x Combine like terms: 3iy + -3iy = 0 -3ix + 3iy + -4x + 9y = 5 + -10I + 0 + -2x -3ix + 3iy + -4x + 9y = 5 + -10I + -2x Add '4x' to each side of the equation. -3ix + 3iy + -4x + 4x + 9y = 5 + -10I + -2x + 4x Combine like terms: -4x + 4x = 0 -3ix + 3iy + 0 + 9y = 5 + -10I + -2x + 4x -3ix + 3iy + 9y = 5 + -10I + -2x + 4x Combine like terms: -2x + 4x = 2x -3ix + 3iy + 9y = 5 + -10I + 2x Add '-9y' to each side of the equation. -3ix + 3iy + 9y + -9y = 5 + -10I + 2x + -9y Combine like terms: 9y + -9y = 0 -3ix + 3iy + 0 = 5 + -10I + 2x + -9y -3ix + 3iy = 5 + -10I + 2x + -9y Reorder the terms: -5 + 10I + -3ix + 3iy + -2x + 9y = 5 + -10I + 2x + -9y + -5 + 10I + -2x + 9y Reorder the terms: -5 + 10I + -3ix + 3iy + -2x + 9y = 5 + -5 + -10I + 10I + 2x + -2x + -9y + 9y Combine like terms: 5 + -5 = 0 -5 + 10I + -3ix + 3iy + -2x + 9y = 0 + -10I + 10I + 2x + -2x + -9y + 9y -5 + 10I + -3ix + 3iy + -2x + 9y = -10I + 10I + 2x + -2x + -9y + 9y Combine like terms: -10I + 10I = 0 -5 + 10I + -3ix + 3iy + -2x + 9y = 0 + 2x + -2x + -9y + 9y -5 + 10I + -3ix + 3iy + -2x + 9y = 2x + -2x + -9y + 9y Combine like terms: 2x + -2x = 0 -5 + 10I + -3ix + 3iy + -2x + 9y = 0 + -9y + 9y -5 + 10I + -3ix + 3iy + -2x + 9y = -9y + 9y Combine like terms: -9y + 9y = 0 -5 + 10I + -3ix + 3iy + -2x + 9y = 0 The solution to this equation could not be determined.
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