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Simplifying 4.2(2x + -0.5y) + -2(4.1x + -0.3y) = 0 (2x * 4.2 + -0.5y * 4.2) + -2(4.1x + -0.3y) = 0 (8.4x + -2.1y) + -2(4.1x + -0.3y) = 0 8.4x + -2.1y + (4.1x * -2 + -0.3y * -2) = 0 8.4x + -2.1y + (-8.2x + 0.6y) = 0 Reorder the terms: 8.4x + -8.2x + -2.1y + 0.6y = 0 Combine like terms: 8.4x + -8.2x = 0.2x 0.2x + -2.1y + 0.6y = 0 Combine like terms: -2.1y + 0.6y = -1.5y 0.2x + -1.5y = 0 Solving 0.2x + -1.5y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5y' to each side of the equation. 0.2x + -1.5y + 1.5y = 0 + 1.5y Combine like terms: -1.5y + 1.5y = 0.0 0.2x + 0.0 = 0 + 1.5y 0.2x = 0 + 1.5y Remove the zero: 0.2x = 1.5y Divide each side by '0.2'. x = 7.5y Simplifying x = 7.5y
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