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Simplifying (8x + -7y)(9x + -5y) = 0 Multiply (8x + -7y) * (9x + -5y) (8x * (9x + -5y) + -7y * (9x + -5y)) = 0 ((9x * 8x + -5y * 8x) + -7y * (9x + -5y)) = 0 Reorder the terms: ((-40xy + 72x2) + -7y * (9x + -5y)) = 0 ((-40xy + 72x2) + -7y * (9x + -5y)) = 0 (-40xy + 72x2 + (9x * -7y + -5y * -7y)) = 0 (-40xy + 72x2 + (-63xy + 35y2)) = 0 Reorder the terms: (-40xy + -63xy + 72x2 + 35y2) = 0 Combine like terms: -40xy + -63xy = -103xy (-103xy + 72x2 + 35y2) = 0 Solving -103xy + 72x2 + 35y2 = 0 Solving for variable 'x'. Factor a trinomial. (8x + -7y)(9x + -5y) = 0Subproblem 1
Set the factor '(8x + -7y)' equal to zero and attempt to solve: Simplifying 8x + -7y = 0 Solving 8x + -7y = 0 Move all terms containing x to the left, all other terms to the right. Add '7y' to each side of the equation. 8x + -7y + 7y = 0 + 7y Combine like terms: -7y + 7y = 0 8x + 0 = 0 + 7y 8x = 0 + 7y Remove the zero: 8x = 7y Divide each side by '8'. x = 0.875y Simplifying x = 0.875ySubproblem 2
Set the factor '(9x + -5y)' equal to zero and attempt to solve: Simplifying 9x + -5y = 0 Solving 9x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 9x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 9x + 0 = 0 + 5y 9x = 0 + 5y Remove the zero: 9x = 5y Divide each side by '9'. x = 0.5555555556y Simplifying x = 0.5555555556ySolution
x = {0.875y, 0.5555555556y}
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