Solve V_{s}=frac{P_{m}V_{m}T_{s}}{P_{s}T_{m}}

$$V _ { s } = \frac { P _ { m } V _ { m } T _ { s } } { P _ { s } T _ { m } }$$

Solve for P_m

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

Steps for Solving Linear Equation

Multiply both sides of the equation by P_{s}T_{m}.

$$V_{s}P_{s}T_{m}=P_{m}V_{m}T_{s}$$

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

$$P_{m}V_{m}T_{s}=V_{s}P_{s}T_{m}$$

The equation is in standard form.

$$T_{s}V_{m}P_{m}=P_{s}T_{m}V_{s}$$

Divide both sides by V_{m}T_{s}.

$$\frac{T_{s}V_{m}P_{m}}{T_{s}V_{m}}=\frac{P_{s}T_{m}V_{s}}{T_{s}V_{m}}$$

Dividing by V_{m}T_{s} undoes the multiplication by V_{m}T_{s}.

$$P_{m}=\frac{P_{s}T_{m}V_{s}}{T_{s}V_{m}}$$

Solve for P_s

$$\left\{\begin{matrix}P_{s}=\frac{P_{m}T_{s}V_{m}}{T_{m}V_{s}}\text{, }&T_{s}\neq 0\text{ and }V_{m}\neq 0\text{ and }P_{m}\neq 0\text{ and }T_{m}\neq 0\text{ and }V_{s}\neq 0\\P_{s}\neq 0\text{, }&\left(T_{s}=0\text{ or }V_{m}=0\text{ or }P_{m}=0\right)\text{ and }V_{s}=0\text{ and }T_{m}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable P_{s} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by P_{s}T_{m}.

$$V_{s}P_{s}T_{m}=P_{m}V_{m}T_{s}$$

Reorder the terms.

$$P_{s}T_{m}V_{s}=P_{m}T_{s}V_{m}$$

The equation is in standard form.

$$T_{m}V_{s}P_{s}=P_{m}T_{s}V_{m}$$

Divide both sides by V_{s}T_{m}.

$$\frac{T_{m}V_{s}P_{s}}{T_{m}V_{s}}=\frac{P_{m}T_{s}V_{m}}{T_{m}V_{s}}$$

Dividing by V_{s}T_{m} undoes the multiplication by V_{s}T_{m}.

$$P_{s}=\frac{P_{m}T_{s}V_{m}}{T_{m}V_{s}}$$

Variable P_{s} cannot be equal to 0.

$$P_{s}=\frac{P_{m}T_{s}V_{m}}{T_{m}V_{s}}\text{, }P_{s}\neq 0$$