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Simplifying 0.5(20x + -50y + 36) + -0.25(-100x + 40y + -12) = 0 Reorder the terms: 0.5(36 + 20x + -50y) + -0.25(-100x + 40y + -12) = 0 (36 * 0.5 + 20x * 0.5 + -50y * 0.5) + -0.25(-100x + 40y + -12) = 0 (18 + 10x + -25y) + -0.25(-100x + 40y + -12) = 0 Reorder the terms: 18 + 10x + -25y + -0.25(-12 + -100x + 40y) = 0 18 + 10x + -25y + (-12 * -0.25 + -100x * -0.25 + 40y * -0.25) = 0 18 + 10x + -25y + (3 + 25x + -10y) = 0 Reorder the terms: 18 + 3 + 10x + 25x + -25y + -10y = 0 Combine like terms: 18 + 3 = 21 21 + 10x + 25x + -25y + -10y = 0 Combine like terms: 10x + 25x = 35x 21 + 35x + -25y + -10y = 0 Combine like terms: -25y + -10y = -35y 21 + 35x + -35y = 0 Solving 21 + 35x + -35y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + 35x + -21 + -35y = 0 + -21 Reorder the terms: 21 + -21 + 35x + -35y = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 35x + -35y = 0 + -21 35x + -35y = 0 + -21 Combine like terms: 0 + -21 = -21 35x + -35y = -21 Add '35y' to each side of the equation. 35x + -35y + 35y = -21 + 35y Combine like terms: -35y + 35y = 0 35x + 0 = -21 + 35y 35x = -21 + 35y Divide each side by '35'. x = -0.6 + y Simplifying x = -0.6 + y
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