Solve P_{1}V_{1}=P_{2}V_{2}

$$P _ { 1 } V _ { 1 } = P _ { 2 } V _ { 2 }$$

Solve for P_1

$$\left\{\begin{matrix}P_{1}=\frac{P_{2}V_{2}}{V_{1}}\text{, }&V_{1}\neq 0\\P_{1}\in \mathrm{R}\text{, }&\left(P_{2}=0\text{ or }V_{2}=0\right)\text{ and }V_{1}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$V_{1}P_{1}=P_{2}V_{2}$$

Divide both sides by V_{1}.

$$\frac{V_{1}P_{1}}{V_{1}}=\frac{P_{2}V_{2}}{V_{1}}$$

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

$$P_{1}=\frac{P_{2}V_{2}}{V_{1}}$$

Solve for P_2

$$\left\{\begin{matrix}P_{2}=\frac{P_{1}V_{1}}{V_{2}}\text{, }&V_{2}\neq 0\\P_{2}\in \mathrm{R}\text{, }&\left(P_{1}=0\text{ or }V_{1}=0\right)\text{ and }V_{2}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$P_{2}V_{2}=P_{1}V_{1}$$

The equation is in standard form.

$$V_{2}P_{2}=P_{1}V_{1}$$

Divide both sides by V_{2}.

$$\frac{V_{2}P_{2}}{V_{2}}=\frac{P_{1}V_{1}}{V_{2}}$$

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

$$P_{2}=\frac{P_{1}V_{1}}{V_{2}}$$