Solve frac{V_{1}}{T_{1}}=frac{V_{2}}{T_{2}}

$$\frac { V _ { 1 } } { T _ { 1 } } = \frac { V _ { 2 } } { T _ { 2 } }$$

Solve for T_1

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

Steps for Solving Linear Equation

Variable T_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by T_{1}T_{2}, the least common multiple of T_{1},T_{2}.

$$T_{2}V_{1}=T_{1}V_{2}$$

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

$$T_{1}V_{2}=T_{2}V_{1}$$

The equation is in standard form.

$$V_{2}T_{1}=T_{2}V_{1}$$

Divide both sides by V_{2}.

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

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

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

Variable T_{1} cannot be equal to 0.

$$T_{1}=\frac{T_{2}V_{1}}{V_{2}}\text{, }T_{1}\neq 0$$

Solve for T_2

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

Steps for Solving Linear Equation

Variable T_{2} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by T_{1}T_{2}, the least common multiple of T_{1},T_{2}.

$$T_{2}V_{1}=T_{1}V_{2}$$

The equation is in standard form.

$$V_{1}T_{2}=T_{1}V_{2}$$

Divide both sides by V_{1}.

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

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

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

Variable T_{2} cannot be equal to 0.

$$T_{2}=\frac{T_{1}V_{2}}{V_{1}}\text{, }T_{2}\neq 0$$