Solve {l}{frac{V_{1}R_{1}}{X_{1}}=frac{V_{2}R_{2}}{X_{2}}}{a=X_{2}}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { \frac{V_{1} R_{1}}{X_{1}} = \frac{V_{2} R_{2}}{X_{2}} }\\ { a = X_{2} }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for V_1, R_1, X_1, V_2, R_2, X_2, a, b

$$V_{1}=\frac{R_{2}V_{2}X_{1}}{R_{1}X_{2}}\text{, }R_{1}\neq 0\text{, }X_{1}\neq 0\text{, }V_{2}\in \mathrm{R}\text{, }R_{2}\in \mathrm{R}\text{, }X_{2}\neq 0\text{, }a=X_{2}\text{, }b=X_{2}$$

$$V_{1}\in \mathrm{R}\text{, }R_{1}=0\text{, }X_{1}\neq 0\text{, }V_{2}\in \mathrm{R}\text{, }R_{2}=0\text{, }X_{2}\neq 0\text{, }a=X_{2}\text{, }b=X_{2}$$

$$V_{1}\in \mathrm{R}\text{, }R_{1}=0\text{, }X_{1}\neq 0\text{, }V_{2}=0\text{, }R_{2}\in \mathrm{R}\text{, }X_{2}\neq 0\text{, }a=X_{2}\text{, }b=X_{2}$$