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Simplifying 2(x + y) + 4(a + b) = 100 (x * 2 + y * 2) + 4(a + b) = 100 (2x + 2y) + 4(a + b) = 100 2x + 2y + (a * 4 + b * 4) = 100 2x + 2y + (4a + 4b) = 100 Reorder the terms: 4a + 4b + 2x + 2y = 100 Solving 4a + 4b + 2x + 2y = 100 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 4a + 4b + 2x + -4b + 2y = 100 + -4b Reorder the terms: 4a + 4b + -4b + 2x + 2y = 100 + -4b Combine like terms: 4b + -4b = 0 4a + 0 + 2x + 2y = 100 + -4b 4a + 2x + 2y = 100 + -4b Add '-2x' to each side of the equation. 4a + 2x + -2x + 2y = 100 + -4b + -2x Combine like terms: 2x + -2x = 0 4a + 0 + 2y = 100 + -4b + -2x 4a + 2y = 100 + -4b + -2x Add '-2y' to each side of the equation. 4a + 2y + -2y = 100 + -4b + -2x + -2y Combine like terms: 2y + -2y = 0 4a + 0 = 100 + -4b + -2x + -2y 4a = 100 + -4b + -2x + -2y Divide each side by '4'. a = 25 + -1b + -0.5x + -0.5y Simplifying a = 25 + -1b + -0.5x + -0.5y
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