Solve 11x=9x/5y+13y

$$11x= \frac{ 9x }{ 5y } +13y$$

Solve for x

$$x=\frac{65y^{2}}{55y-9}$$

$$y\neq \frac{9}{55}\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5y.

$$11x\times 5y=9x+13y\times 5y$$

Multiply 11 and 5 to get 55.

$$55xy=9x+13y\times 5y$$

Multiply y and y to get y^{2}.

$$55xy=9x+13y^{2}\times 5$$

Multiply 13 and 5 to get 65.

$$55xy=9x+65y^{2}$$

Subtract 9x from both sides.

$$55xy-9x=65y^{2}$$

Combine all terms containing x.

$$\left(55y-9\right)x=65y^{2}$$

Divide both sides by 55y-9.

$$\frac{\left(55y-9\right)x}{55y-9}=\frac{65y^{2}}{55y-9}$$

Dividing by 55y-9 undoes the multiplication by 55y-9.

$$x=\frac{65y^{2}}{55y-9}$$

Solve for y (complex solution)

$$y=-\frac{\sqrt{3025x^{2}-2340x}}{130}+\frac{11x}{26}$$

$$y=\frac{\sqrt{3025x^{2}-2340x}}{130}+\frac{11x}{26}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{\sqrt{3025x^{2}-2340x}}{130}+\frac{11x}{26}$$

$$y=\frac{\sqrt{3025x^{2}-2340x}}{130}+\frac{11x}{26}\text{, }x\geq \frac{468}{605}\text{ or }x<0$$