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Simplifying (4x + -3)(y + -5) + (3 + -2x)(5 + -1y) = 0 Reorder the terms: (-3 + 4x)(y + -5) + (3 + -2x)(5 + -1y) = 0 Reorder the terms: (-3 + 4x)(-5 + y) + (3 + -2x)(5 + -1y) = 0 Multiply (-3 + 4x) * (-5 + y) (-3(-5 + y) + 4x * (-5 + y)) + (3 + -2x)(5 + -1y) = 0 ((-5 * -3 + y * -3) + 4x * (-5 + y)) + (3 + -2x)(5 + -1y) = 0 ((15 + -3y) + 4x * (-5 + y)) + (3 + -2x)(5 + -1y) = 0 (15 + -3y + (-5 * 4x + y * 4x)) + (3 + -2x)(5 + -1y) = 0 (15 + -3y + (-20x + 4xy)) + (3 + -2x)(5 + -1y) = 0 Reorder the terms: (15 + -20x + 4xy + -3y) + (3 + -2x)(5 + -1y) = 0 (15 + -20x + 4xy + -3y) + (3 + -2x)(5 + -1y) = 0 Multiply (3 + -2x) * (5 + -1y) 15 + -20x + 4xy + -3y + (3(5 + -1y) + -2x * (5 + -1y)) = 0 15 + -20x + 4xy + -3y + ((5 * 3 + -1y * 3) + -2x * (5 + -1y)) = 0 15 + -20x + 4xy + -3y + ((15 + -3y) + -2x * (5 + -1y)) = 0 15 + -20x + 4xy + -3y + (15 + -3y + (5 * -2x + -1y * -2x)) = 0 15 + -20x + 4xy + -3y + (15 + -3y + (-10x + 2xy)) = 0 Reorder the terms: 15 + -20x + 4xy + -3y + (15 + -10x + 2xy + -3y) = 0 15 + -20x + 4xy + -3y + (15 + -10x + 2xy + -3y) = 0 Reorder the terms: 15 + 15 + -20x + -10x + 4xy + 2xy + -3y + -3y = 0 Combine like terms: 15 + 15 = 30 30 + -20x + -10x + 4xy + 2xy + -3y + -3y = 0 Combine like terms: -20x + -10x = -30x 30 + -30x + 4xy + 2xy + -3y + -3y = 0 Combine like terms: 4xy + 2xy = 6xy 30 + -30x + 6xy + -3y + -3y = 0 Combine like terms: -3y + -3y = -6y 30 + -30x + 6xy + -6y = 0 Solving 30 + -30x + 6xy + -6y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30x + 6xy + -30 + -6y = 0 + -30 Reorder the terms: 30 + -30 + -30x + 6xy + -6y = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -30x + 6xy + -6y = 0 + -30 -30x + 6xy + -6y = 0 + -30 Combine like terms: 0 + -30 = -30 -30x + 6xy + -6y = -30 Add '6y' to each side of the equation. -30x + 6xy + -6y + 6y = -30 + 6y Combine like terms: -6y + 6y = 0 -30x + 6xy + 0 = -30 + 6y -30x + 6xy = -30 + 6y Reorder the terms: 30 + -30x + 6xy + -6y = -30 + 6y + 30 + -6y Reorder the terms: 30 + -30x + 6xy + -6y = -30 + 30 + 6y + -6y Combine like terms: -30 + 30 = 0 30 + -30x + 6xy + -6y = 0 + 6y + -6y 30 + -30x + 6xy + -6y = 6y + -6y Combine like terms: 6y + -6y = 0 30 + -30x + 6xy + -6y = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(5 + -5x + xy + -1y) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(5 + -5x + xy + -1y)' equal to zero and attempt to solve: Simplifying 5 + -5x + xy + -1y = 0 Solving 5 + -5x + xy + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5x + xy + -5 + -1y = 0 + -5 Reorder the terms: 5 + -5 + -5x + xy + -1y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5x + xy + -1y = 0 + -5 -5x + xy + -1y = 0 + -5 Combine like terms: 0 + -5 = -5 -5x + xy + -1y = -5 Add 'y' to each side of the equation. -5x + xy + -1y + y = -5 + y Combine like terms: -1y + y = 0 -5x + xy + 0 = -5 + y -5x + xy = -5 + y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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