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Simplifying 5(x + -1z) + 4(y + -1x) = 0 (x * 5 + -1z * 5) + 4(y + -1x) = 0 (5x + -5z) + 4(y + -1x) = 0 Reorder the terms: 5x + -5z + 4(-1x + y) = 0 5x + -5z + (-1x * 4 + y * 4) = 0 5x + -5z + (-4x + 4y) = 0 Reorder the terms: 5x + -4x + 4y + -5z = 0 Combine like terms: 5x + -4x = 1x 1x + 4y + -5z = 0 Solving 1x + 4y + -5z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 1x + 4y + -4y + -5z = 0 + -4y Combine like terms: 4y + -4y = 0 1x + 0 + -5z = 0 + -4y 1x + -5z = 0 + -4y Remove the zero: 1x + -5z = -4y Add '5z' to each side of the equation. 1x + -5z + 5z = -4y + 5z Combine like terms: -5z + 5z = 0 1x + 0 = -4y + 5z 1x = -4y + 5z Divide each side by '1'. x = -4y + 5z Simplifying x = -4y + 5z
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