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