Solve 2xy/x^2=y^2/k

$$\frac { 2 x y } { x ^ { 2 } } = \frac { y ^ { 2 } } { k }$$

Solve for k

$$\left\{\begin{matrix}k=\frac{xy}{2}\text{, }&x\neq 0\text{ and }y\neq 0\\k\neq 0\text{, }&y=0\text{ and }x\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by kx^{2}, the least common multiple of x^{2},k.

$$k\times 2xy=x^{2}y^{2}$$

Reorder the terms.

$$2kxy=x^{2}y^{2}$$

The equation is in standard form.

$$2xyk=x^{2}y^{2}$$

Divide both sides by 2xy.

$$\frac{2xyk}{2xy}=\frac{x^{2}y^{2}}{2xy}$$

Dividing by 2xy undoes the multiplication by 2xy.

$$k=\frac{x^{2}y^{2}}{2xy}$$

Divide x^{2}y^{2} by 2xy.

$$k=\frac{xy}{2}$$

Variable k cannot be equal to 0.

$$k=\frac{xy}{2}\text{, }k\neq 0$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2k}{y}\text{, }&k\neq 0\text{ and }y\neq 0\\x\neq 0\text{, }&y=0\text{ and }k\neq 0\end{matrix}\right.$$