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Simplifying (2x + -5y)(3x + -1y) = 0 Multiply (2x + -5y) * (3x + -1y) (2x * (3x + -1y) + -5y * (3x + -1y)) = 0 ((3x * 2x + -1y * 2x) + -5y * (3x + -1y)) = 0 Reorder the terms: ((-2xy + 6x2) + -5y * (3x + -1y)) = 0 ((-2xy + 6x2) + -5y * (3x + -1y)) = 0 (-2xy + 6x2 + (3x * -5y + -1y * -5y)) = 0 (-2xy + 6x2 + (-15xy + 5y2)) = 0 Reorder the terms: (-2xy + -15xy + 6x2 + 5y2) = 0 Combine like terms: -2xy + -15xy = -17xy (-17xy + 6x2 + 5y2) = 0 Solving -17xy + 6x2 + 5y2 = 0 Solving for variable 'x'. Factor a trinomial. (2x + -5y)(3x + -1y) = 0Subproblem 1
Set the factor '(2x + -5y)' equal to zero and attempt to solve: Simplifying 2x + -5y = 0 Solving 2x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 2x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 2x + 0 = 0 + 5y 2x = 0 + 5y Remove the zero: 2x = 5y Divide each side by '2'. x = 2.5y Simplifying x = 2.5ySubproblem 2
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 = 0.3333333333ySolution
x = {2.5y, 0.3333333333y}
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