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Simplifying 5(2y + -3x) + 7(4x + -5y + 3) = 0 Reorder the terms: 5(-3x + 2y) + 7(4x + -5y + 3) = 0 (-3x * 5 + 2y * 5) + 7(4x + -5y + 3) = 0 (-15x + 10y) + 7(4x + -5y + 3) = 0 Reorder the terms: -15x + 10y + 7(3 + 4x + -5y) = 0 -15x + 10y + (3 * 7 + 4x * 7 + -5y * 7) = 0 -15x + 10y + (21 + 28x + -35y) = 0 Reorder the terms: 21 + -15x + 28x + 10y + -35y = 0 Combine like terms: -15x + 28x = 13x 21 + 13x + 10y + -35y = 0 Combine like terms: 10y + -35y = -25y 21 + 13x + -25y = 0 Solving 21 + 13x + -25y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + 13x + -21 + -25y = 0 + -21 Reorder the terms: 21 + -21 + 13x + -25y = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 13x + -25y = 0 + -21 13x + -25y = 0 + -21 Combine like terms: 0 + -21 = -21 13x + -25y = -21 Add '25y' to each side of the equation. 13x + -25y + 25y = -21 + 25y Combine like terms: -25y + 25y = 0 13x + 0 = -21 + 25y 13x = -21 + 25y Divide each side by '13'. x = -1.615384615 + 1.923076923y Simplifying x = -1.615384615 + 1.923076923y
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