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Simplifying 5(2x + 3y) + -4(3x + -5y) = 0 (2x * 5 + 3y * 5) + -4(3x + -5y) = 0 (10x + 15y) + -4(3x + -5y) = 0 10x + 15y + (3x * -4 + -5y * -4) = 0 10x + 15y + (-12x + 20y) = 0 Reorder the terms: 10x + -12x + 15y + 20y = 0 Combine like terms: 10x + -12x = -2x -2x + 15y + 20y = 0 Combine like terms: 15y + 20y = 35y -2x + 35y = 0 Solving -2x + 35y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35y' to each side of the equation. -2x + 35y + -35y = 0 + -35y Combine like terms: 35y + -35y = 0 -2x + 0 = 0 + -35y -2x = 0 + -35y Remove the zero: -2x = -35y Divide each side by '-2'. x = 17.5y Simplifying x = 17.5y
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