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Simplifying (8b + -10c + 3a + -1d) + -1(2xy + 4y + -3x) = 0 Reorder the terms: (3a + 8b + -10c + -1d) + -1(2xy + 4y + -3x) = 0 Remove parenthesis around (3a + 8b + -10c + -1d) 3a + 8b + -10c + -1d + -1(2xy + 4y + -3x) = 0 Reorder the terms: 3a + 8b + -10c + -1d + -1(-3x + 2xy + 4y) = 0 3a + 8b + -10c + -1d + (-3x * -1 + 2xy * -1 + 4y * -1) = 0 3a + 8b + -10c + -1d + (3x + -2xy + -4y) = 0 Solving 3a + 8b + -10c + -1d + 3x + -2xy + -4y = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8b' to each side of the equation. 3a + 8b + -10c + -1d + 3x + -2xy + -8b + -4y = 0 + -8b Reorder the terms: 3a + 8b + -8b + -10c + -1d + 3x + -2xy + -4y = 0 + -8b Combine like terms: 8b + -8b = 0 3a + 0 + -10c + -1d + 3x + -2xy + -4y = 0 + -8b 3a + -10c + -1d + 3x + -2xy + -4y = 0 + -8b Remove the zero: 3a + -10c + -1d + 3x + -2xy + -4y = -8b Add '10c' to each side of the equation. 3a + -10c + -1d + 3x + -2xy + 10c + -4y = -8b + 10c Reorder the terms: 3a + -10c + 10c + -1d + 3x + -2xy + -4y = -8b + 10c Combine like terms: -10c + 10c = 0 3a + 0 + -1d + 3x + -2xy + -4y = -8b + 10c 3a + -1d + 3x + -2xy + -4y = -8b + 10c Add 'd' to each side of the equation. 3a + -1d + 3x + -2xy + d + -4y = -8b + 10c + d Reorder the terms: 3a + -1d + d + 3x + -2xy + -4y = -8b + 10c + d Combine like terms: -1d + d = 0 3a + 0 + 3x + -2xy + -4y = -8b + 10c + d 3a + 3x + -2xy + -4y = -8b + 10c + d Add '-3x' to each side of the equation. 3a + 3x + -2xy + -3x + -4y = -8b + 10c + d + -3x Reorder the terms: 3a + 3x + -3x + -2xy + -4y = -8b + 10c + d + -3x Combine like terms: 3x + -3x = 0 3a + 0 + -2xy + -4y = -8b + 10c + d + -3x 3a + -2xy + -4y = -8b + 10c + d + -3x Add '2xy' to each side of the equation. 3a + -2xy + 2xy + -4y = -8b + 10c + d + -3x + 2xy Combine like terms: -2xy + 2xy = 0 3a + 0 + -4y = -8b + 10c + d + -3x + 2xy 3a + -4y = -8b + 10c + d + -3x + 2xy Add '4y' to each side of the equation. 3a + -4y + 4y = -8b + 10c + d + -3x + 2xy + 4y Combine like terms: -4y + 4y = 0 3a + 0 = -8b + 10c + d + -3x + 2xy + 4y 3a = -8b + 10c + d + -3x + 2xy + 4y Divide each side by '3'. a = -2.666666667b + 3.333333333c + 0.3333333333d + -1x + 0.6666666667xy + 1.333333333y Simplifying a = -2.666666667b + 3.333333333c + 0.3333333333d + -1x + 0.6666666667xy + 1.333333333y
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