Solve 125%xdivy=x

$$125 \% x \div y=x$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&y=\frac{5}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$\frac{125}{100}x=xy$$

Reduce the fraction \frac{125}{100} to lowest terms by extracting and canceling out 25.

$$\frac{5}{4}x=xy$$

Subtract xy from both sides.

$$\frac{5}{4}x-xy=0$$

Combine all terms containing x.

$$\left(\frac{5}{4}-y\right)x=0$$

Divide 0 by \frac{5}{4}-y.

$$x=0$$

Solve for x

$$\left\{\begin{matrix}x=0\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&y=\frac{5}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$\frac{125}{100}x=xy$$

Reduce the fraction \frac{125}{100} to lowest terms by extracting and canceling out 25.

$$\frac{5}{4}x=xy$$

Subtract xy from both sides.

$$\frac{5}{4}x-xy=0$$

Combine all terms containing x.

$$\left(\frac{5}{4}-y\right)x=0$$

Divide 0 by \frac{5}{4}-y.

$$x=0$$

Solve for y

$$\left\{\begin{matrix}\\y=\frac{5}{4}\text{, }&\text{unconditionally}\\y\neq 0\text{, }&x=0\end{matrix}\right.$$

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 y.

$$\frac{125}{100}x=xy$$

Reduce the fraction \frac{125}{100} to lowest terms by extracting and canceling out 25.

$$\frac{5}{4}x=xy$$

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

$$xy=\frac{5}{4}x$$

The equation is in standard form.

$$xy=\frac{5x}{4}$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{5x}{4x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{5x}{4x}$$

Divide \frac{5x}{4} by x.

$$y=\frac{5}{4}$$