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Simplifying 7000x + 3500y + 1000(1 + -1x + -1y) = 2500x + 3500y + 4000(1 + -1x + -1y) 7000x + 3500y + (1 * 1000 + -1x * 1000 + -1y * 1000) = 2500x + 3500y + 4000(1 + -1x + -1y) 7000x + 3500y + (1000 + -1000x + -1000y) = 2500x + 3500y + 4000(1 + -1x + -1y) Reorder the terms: 1000 + 7000x + -1000x + 3500y + -1000y = 2500x + 3500y + 4000(1 + -1x + -1y) Combine like terms: 7000x + -1000x = 6000x 1000 + 6000x + 3500y + -1000y = 2500x + 3500y + 4000(1 + -1x + -1y) Combine like terms: 3500y + -1000y = 2500y 1000 + 6000x + 2500y = 2500x + 3500y + 4000(1 + -1x + -1y) 1000 + 6000x + 2500y = 2500x + 3500y + (1 * 4000 + -1x * 4000 + -1y * 4000) 1000 + 6000x + 2500y = 2500x + 3500y + (4000 + -4000x + -4000y) Reorder the terms: 1000 + 6000x + 2500y = 4000 + 2500x + -4000x + 3500y + -4000y Combine like terms: 2500x + -4000x = -1500x 1000 + 6000x + 2500y = 4000 + -1500x + 3500y + -4000y Combine like terms: 3500y + -4000y = -500y 1000 + 6000x + 2500y = 4000 + -1500x + -500y Solving 1000 + 6000x + 2500y = 4000 + -1500x + -500y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1500x' to each side of the equation. 1000 + 6000x + 1500x + 2500y = 4000 + -1500x + 1500x + -500y Combine like terms: 6000x + 1500x = 7500x 1000 + 7500x + 2500y = 4000 + -1500x + 1500x + -500y Combine like terms: -1500x + 1500x = 0 1000 + 7500x + 2500y = 4000 + 0 + -500y 1000 + 7500x + 2500y = 4000 + -500y Add '-1000' to each side of the equation. 1000 + 7500x + -1000 + 2500y = 4000 + -1000 + -500y Reorder the terms: 1000 + -1000 + 7500x + 2500y = 4000 + -1000 + -500y Combine like terms: 1000 + -1000 = 0 0 + 7500x + 2500y = 4000 + -1000 + -500y 7500x + 2500y = 4000 + -1000 + -500y Combine like terms: 4000 + -1000 = 3000 7500x + 2500y = 3000 + -500y Add '-2500y' to each side of the equation. 7500x + 2500y + -2500y = 3000 + -500y + -2500y Combine like terms: 2500y + -2500y = 0 7500x + 0 = 3000 + -500y + -2500y 7500x = 3000 + -500y + -2500y Combine like terms: -500y + -2500y = -3000y 7500x = 3000 + -3000y Divide each side by '7500'. x = 0.4 + -0.4y Simplifying x = 0.4 + -0.4y
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