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Simplifying 7000x + 3500y + 1000(1 + -1x + -1y) = 4000x + 4000y + 3000(1 + -1x + -1y) 7000x + 3500y + (1 * 1000 + -1x * 1000 + -1y * 1000) = 4000x + 4000y + 3000(1 + -1x + -1y) 7000x + 3500y + (1000 + -1000x + -1000y) = 4000x + 4000y + 3000(1 + -1x + -1y) Reorder the terms: 1000 + 7000x + -1000x + 3500y + -1000y = 4000x + 4000y + 3000(1 + -1x + -1y) Combine like terms: 7000x + -1000x = 6000x 1000 + 6000x + 3500y + -1000y = 4000x + 4000y + 3000(1 + -1x + -1y) Combine like terms: 3500y + -1000y = 2500y 1000 + 6000x + 2500y = 4000x + 4000y + 3000(1 + -1x + -1y) 1000 + 6000x + 2500y = 4000x + 4000y + (1 * 3000 + -1x * 3000 + -1y * 3000) 1000 + 6000x + 2500y = 4000x + 4000y + (3000 + -3000x + -3000y) Reorder the terms: 1000 + 6000x + 2500y = 3000 + 4000x + -3000x + 4000y + -3000y Combine like terms: 4000x + -3000x = 1000x 1000 + 6000x + 2500y = 3000 + 1000x + 4000y + -3000y Combine like terms: 4000y + -3000y = 1000y 1000 + 6000x + 2500y = 3000 + 1000x + 1000y Solving 1000 + 6000x + 2500y = 3000 + 1000x + 1000y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1000x' to each side of the equation. 1000 + 6000x + -1000x + 2500y = 3000 + 1000x + -1000x + 1000y Combine like terms: 6000x + -1000x = 5000x 1000 + 5000x + 2500y = 3000 + 1000x + -1000x + 1000y Combine like terms: 1000x + -1000x = 0 1000 + 5000x + 2500y = 3000 + 0 + 1000y 1000 + 5000x + 2500y = 3000 + 1000y Add '-1000' to each side of the equation. 1000 + 5000x + -1000 + 2500y = 3000 + -1000 + 1000y Reorder the terms: 1000 + -1000 + 5000x + 2500y = 3000 + -1000 + 1000y Combine like terms: 1000 + -1000 = 0 0 + 5000x + 2500y = 3000 + -1000 + 1000y 5000x + 2500y = 3000 + -1000 + 1000y Combine like terms: 3000 + -1000 = 2000 5000x + 2500y = 2000 + 1000y Add '-2500y' to each side of the equation. 5000x + 2500y + -2500y = 2000 + 1000y + -2500y Combine like terms: 2500y + -2500y = 0 5000x + 0 = 2000 + 1000y + -2500y 5000x = 2000 + 1000y + -2500y Combine like terms: 1000y + -2500y = -1500y 5000x = 2000 + -1500y Divide each side by '5000'. x = 0.4 + -0.3y Simplifying x = 0.4 + -0.3y
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