Solve x1/x2=y1/y2

$$\frac{ x1 }{ x2 } = \frac{ y1 }{ y2 }$$

Solve for x_1

$$x_{1}=\frac{x_{2}y_{1}}{y_{2}}$$

$$x_{2}\neq 0\text{ and }y_{2}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x_{2}y_{2}, the least common multiple of x_{2},y_{2}.

$$y_{2}x_{1}=x_{2}y_{1}$$

Divide both sides by y_{2}.

$$\frac{y_{2}x_{1}}{y_{2}}=\frac{x_{2}y_{1}}{y_{2}}$$

Dividing by y_{2} undoes the multiplication by y_{2}.

$$x_{1}=\frac{x_{2}y_{1}}{y_{2}}$$

Solve for x_2

$$\left\{\begin{matrix}x_{2}=\frac{x_{1}y_{2}}{y_{1}}\text{, }&y_{2}\neq 0\text{ and }x_{1}\neq 0\text{ and }y_{1}\neq 0\\x_{2}\neq 0\text{, }&y_{1}=0\text{ and }x_{1}=0\text{ and }y_{2}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$y_{2}x_{1}=x_{2}y_{1}$$

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

$$x_{2}y_{1}=y_{2}x_{1}$$

The equation is in standard form.

$$y_{1}x_{2}=x_{1}y_{2}$$

Divide both sides by y_{1}.

$$\frac{y_{1}x_{2}}{y_{1}}=\frac{x_{1}y_{2}}{y_{1}}$$

Dividing by y_{1} undoes the multiplication by y_{1}.

$$x_{2}=\frac{x_{1}y_{2}}{y_{1}}$$

Variable x_{2} cannot be equal to 0.

$$x_{2}=\frac{x_{1}y_{2}}{y_{1}}\text{, }x_{2}\neq 0$$