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Simplifying (4x + -1y)(9x + -4y) = 0 Multiply (4x + -1y) * (9x + -4y) (4x * (9x + -4y) + -1y * (9x + -4y)) = 0 ((9x * 4x + -4y * 4x) + -1y * (9x + -4y)) = 0 Reorder the terms: ((-16xy + 36x2) + -1y * (9x + -4y)) = 0 ((-16xy + 36x2) + -1y * (9x + -4y)) = 0 (-16xy + 36x2 + (9x * -1y + -4y * -1y)) = 0 (-16xy + 36x2 + (-9xy + 4y2)) = 0 Reorder the terms: (-16xy + -9xy + 36x2 + 4y2) = 0 Combine like terms: -16xy + -9xy = -25xy (-25xy + 36x2 + 4y2) = 0 Solving -25xy + 36x2 + 4y2 = 0 Solving for variable 'x'. Factor a trinomial. (9x + -4y)(4x + -1y) = 0Subproblem 1
Set the factor '(9x + -4y)' equal to zero and attempt to solve: Simplifying 9x + -4y = 0 Solving 9x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. 9x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 9x + 0 = 0 + 4y 9x = 0 + 4y Remove the zero: 9x = 4y Divide each side by '9'. x = 0.4444444444y Simplifying x = 0.4444444444ySubproblem 2
Set the factor '(4x + -1y)' equal to zero and attempt to solve: Simplifying 4x + -1y = 0 Solving 4x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 4x + -1y + y = 0 + y Combine like terms: -1y + y = 0 4x + 0 = 0 + y 4x = 0 + y Remove the zero: 4x = y Divide each side by '4'. x = 0.25y Simplifying x = 0.25ySolution
x = {0.4444444444y, 0.25y}
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