Solve 16.1V=18.8v*frac{R_{1}}{R_{1}+21Omega}

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

Solve for V

$$V=\frac{94R_{1}v}{5\times \frac{161R_{1}+3381\Omega }{10}}$$

$$R_{1}\neq -21\Omega$$

Steps for Solving Linear Equation

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

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

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

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

Combine all terms containing V.

$$\left(16.1R_{1}+338.1\Omega \right)V=18.8vR_{1}$$

The equation is in standard form.

$$\frac{161R_{1}+3381\Omega }{10}V=\frac{94R_{1}v}{5}$$

Divide both sides by 16.1R_{1}+338.1\Omega .

$$\frac{10\times \frac{161R_{1}+3381\Omega }{10}V}{161R_{1}+3381\Omega }=\frac{94R_{1}v}{5\times \frac{161R_{1}+3381\Omega }{10}}$$

Dividing by 16.1R_{1}+338.1\Omega undoes the multiplication by 16.1R_{1}+338.1\Omega .

$$V=\frac{94R_{1}v}{5\times \frac{161R_{1}+3381\Omega }{10}}$$

Solve for R_1

$$\left\{\begin{matrix}\\R_{1}\neq 0\text{, }&\text{unconditionally}\\R_{1}=\frac{3381V\Omega }{188v-161V}\text{, }&\Omega \neq 0\text{ and }v\neq 0\text{ and }V\neq \frac{188v}{161}\\R_{1}\neq -21\Omega \text{, }&V=0\text{ and }v=0\end{matrix}\right.$$