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Simplifying (3x + -1y)(5x + y) = 0 Multiply (3x + -1y) * (5x + y) (3x * (5x + y) + -1y * (5x + y)) = 0 ((5x * 3x + y * 3x) + -1y * (5x + y)) = 0 Reorder the terms: ((3xy + 15x2) + -1y * (5x + y)) = 0 ((3xy + 15x2) + -1y * (5x + y)) = 0 (3xy + 15x2 + (5x * -1y + y * -1y)) = 0 (3xy + 15x2 + (-5xy + -1y2)) = 0 Reorder the terms: (3xy + -5xy + 15x2 + -1y2) = 0 Combine like terms: 3xy + -5xy = -2xy (-2xy + 15x2 + -1y2) = 0 Solving -2xy + 15x2 + -1y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -1y)(5x + y) = 0Subproblem 1
Set the factor '(3x + -1y)' equal to zero and attempt to solve: Simplifying 3x + -1y = 0 Solving 3x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 3x + -1y + y = 0 + y Combine like terms: -1y + y = 0 3x + 0 = 0 + y 3x = 0 + y Remove the zero: 3x = y Divide each side by '3'. x = 0.3333333333y Simplifying x = 0.3333333333ySubproblem 2
Set the factor '(5x + y)' equal to zero and attempt to solve: Simplifying 5x + y = 0 Solving 5x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 5x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 5x + 0 = 0 + -1y 5x = 0 + -1y Remove the zero: 5x = -1y Divide each side by '5'. x = -0.2y Simplifying x = -0.2ySolution
x = {0.3333333333y, -0.2y}
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