Solve 16.1V=18.8V*frac{R_{1}}{R_{1}+21.Omega_{2}}

$$16.1 V = 18.8 V \cdot \frac { R _ { 1 } } { R _ { 1 } + 21 . \Omega _ { 2 } }$$

Solve for V

$$\left\{\begin{matrix}\\V=0\text{, }&\text{unconditionally}\\V\in \mathrm{R}\text{, }&R_{1}=\frac{1127\Omega _{2}}{9}\text{ and }\Omega _{2}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R_{1}+21\Omega _{2}.

$$16.1V\left(R_{1}+21\Omega _{2}\right)=18.8VR_{1}$$

Use the distributive property to multiply 16.1V by R_{1}+21\Omega _{2}.

$$16.1VR_{1}+338.1V\Omega _{2}=18.8VR_{1}$$

Subtract 18.8VR_{1} from both sides.

$$16.1VR_{1}+338.1V\Omega _{2}-18.8VR_{1}=0$$

Combine 16.1VR_{1} and -18.8VR_{1} to get -2.7VR_{1}.

$$-2.7VR_{1}+338.1V\Omega _{2}=0$$

Combine all terms containing V.

$$\left(-2.7R_{1}+338.1\Omega _{2}\right)V=0$$

The equation is in standard form.

$$\frac{3381\Omega _{2}-27R_{1}}{10}V=0$$

Divide 0 by -2.7R_{1}+338.1\Omega _{2}.

$$V=0$$

Solve for R_1

$$\left\{\begin{matrix}R_{1}=\frac{1127\Omega _{2}}{9}\text{, }&\Omega _{2}\neq 0\\R_{1}\neq -21\Omega _{2}\text{, }&V=0\end{matrix}\right.$$