Solve 7*x/5y=xy

$$\frac { 7 \times x } { 5 y } = x y$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&y=-\frac{\sqrt{35}}{5}\text{ or }y=\frac{\sqrt{35}}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5y.

$$7x=xy\times 5y$$

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

$$7x=xy^{2}\times 5$$

Subtract xy^{2}\times 5 from both sides.

$$7x-xy^{2}\times 5=0$$

Multiply -1 and 5 to get -5.

$$7x-5xy^{2}=0$$

Combine all terms containing x.

$$\left(7-5y^{2}\right)x=0$$

Divide 0 by 7-5y^{2}.

$$x=0$$

Solve for x

$$\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&|y|=\frac{\sqrt{35}}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5y.

$$7x=xy\times 5y$$

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

$$7x=xy^{2}\times 5$$

Subtract xy^{2}\times 5 from both sides.

$$7x-xy^{2}\times 5=0$$

Multiply -1 and 5 to get -5.

$$7x-5xy^{2}=0$$

Combine all terms containing x.

$$\left(7-5y^{2}\right)x=0$$

Divide 0 by 7-5y^{2}.

$$x=0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=-\frac{\sqrt{35}}{5}\text{; }y=\frac{\sqrt{35}}{5}\text{, }&\text{unconditionally}\\y\neq 0\text{, }&x=0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}\\y=\frac{\sqrt{35}}{5}\text{; }y=-\frac{\sqrt{35}}{5}\text{, }&\text{unconditionally}\\y\neq 0\text{, }&x=0\end{matrix}\right.$$