Solve x/y=x/2

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&y=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y, the least common multiple of y,2.

$$2x=yx$$

Subtract yx from both sides.

$$2x-yx=0$$

Combine all terms containing x.

$$\left(2-y\right)x=0$$

Divide 0 by 2-y.

$$x=0$$

Solve for x

$$\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&y=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2y, the least common multiple of y,2.

$$2x=yx$$

Subtract yx from both sides.

$$2x-yx=0$$

Combine all terms containing x.

$$\left(2-y\right)x=0$$

Divide 0 by 2-y.

$$x=0$$

Solve for y

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

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2y, the least common multiple of y,2.

$$2x=yx$$

Swap sides so that all variable terms are on the left hand side.

$$yx=2x$$

The equation is in standard form.

$$xy=2x$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide 2x by x.

$$y=2$$