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Simplifying x(2k + 1g) + y(4k + 1g) = 10 Reorder the terms: x(1g + 2k) + y(4k + 1g) = 10 (1g * x + 2k * x) + y(4k + 1g) = 10 (1gx + 2kx) + y(4k + 1g) = 10 Reorder the terms: 1gx + 2kx + y(1g + 4k) = 10 1gx + 2kx + (1g * y + 4k * y) = 10 1gx + 2kx + (1gy + 4ky) = 10 Reorder the terms: 1gx + 1gy + 2kx + 4ky = 10 Solving 1gx + 1gy + 2kx + 4ky = 10 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2kx' to each side of the equation. 1gx + 1gy + 2kx + -2kx + 4ky = 10 + -2kx Combine like terms: 2kx + -2kx = 0 1gx + 1gy + 0 + 4ky = 10 + -2kx 1gx + 1gy + 4ky = 10 + -2kx Add '-4ky' to each side of the equation. 1gx + 1gy + 4ky + -4ky = 10 + -2kx + -4ky Combine like terms: 4ky + -4ky = 0 1gx + 1gy + 0 = 10 + -2kx + -4ky 1gx + 1gy = 10 + -2kx + -4ky Reorder the terms: -10 + 1gx + 1gy + 2kx + 4ky = 10 + -2kx + -4ky + -10 + 2kx + 4ky Reorder the terms: -10 + 1gx + 1gy + 2kx + 4ky = 10 + -10 + -2kx + 2kx + -4ky + 4ky Combine like terms: 10 + -10 = 0 -10 + 1gx + 1gy + 2kx + 4ky = 0 + -2kx + 2kx + -4ky + 4ky -10 + 1gx + 1gy + 2kx + 4ky = -2kx + 2kx + -4ky + 4ky Combine like terms: -2kx + 2kx = 0 -10 + 1gx + 1gy + 2kx + 4ky = 0 + -4ky + 4ky -10 + 1gx + 1gy + 2kx + 4ky = -4ky + 4ky Combine like terms: -4ky + 4ky = 0 -10 + 1gx + 1gy + 2kx + 4ky = 0 The solution to this equation could not be determined.
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