9x^2+4y^2=13xy

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Solution for 9x^2+4y^2=13xy equation: 


Simplifying
9x2 + 4y2 = 13xy

Solving
9x2 + 4y2 = 13xy

Solving for variable 'x'.

Reorder the terms:
-13xy + 9x2 + 4y2 = 13xy + -13xy

Combine like terms: 13xy + -13xy = 0
-13xy + 9x2 + 4y2 = 0

Factor a trinomial.
(x + -1y)(9x + -4y) = 0


Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

Move all terms containing x to the left, all other terms to the right.

Add 'y' to each side of the equation.
x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
x + 0 = 0 + y
x = 0 + y
Remove the zero:
x = y

Simplifying
x = y

Subproblem 2
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 = 0.4444444444y
Solution
x = {y, 0.4444444444y}

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