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Simplifying 5(2x + 3y) + 6(y + x) = 0 (2x * 5 + 3y * 5) + 6(y + x) = 0 (10x + 15y) + 6(y + x) = 0 Reorder the terms: 10x + 15y + 6(x + y) = 0 10x + 15y + (x * 6 + y * 6) = 0 10x + 15y + (6x + 6y) = 0 Reorder the terms: 10x + 6x + 15y + 6y = 0 Combine like terms: 10x + 6x = 16x 16x + 15y + 6y = 0 Combine like terms: 15y + 6y = 21y 16x + 21y = 0 Solving 16x + 21y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21y' to each side of the equation. 16x + 21y + -21y = 0 + -21y Combine like terms: 21y + -21y = 0 16x + 0 = 0 + -21y 16x = 0 + -21y Remove the zero: 16x = -21y Divide each side by '16'. x = -1.3125y Simplifying x = -1.3125y
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