Solve I_{T}=V/2R_{1}+V/10

$$I _ { T } = \frac { V } { 2 R _ { 1 } } + \frac { V } { 10 }$$

Solve for R_1

$$\left\{\begin{matrix}R_{1}=-\frac{5V}{V-10I_{T}}\text{, }&V\neq 0\text{ and }I_{T}\neq \frac{V}{10}\\R_{1}\neq 0\text{, }&I_{T}=0\text{ and }V=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable R_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 10R_{1}, the least common multiple of 2R_{1},10.

$$I_{T}\times 10R_{1}=5V+R_{1}V$$

Subtract R_{1}V from both sides.

$$I_{T}\times 10R_{1}-R_{1}V=5V$$

Combine all terms containing R_{1}.

$$\left(I_{T}\times 10-V\right)R_{1}=5V$$

The equation is in standard form.

$$\left(10I_{T}-V\right)R_{1}=5V$$

Divide both sides by 10I_{T}-V.

$$\frac{\left(10I_{T}-V\right)R_{1}}{10I_{T}-V}=\frac{5V}{10I_{T}-V}$$

Dividing by 10I_{T}-V undoes the multiplication by 10I_{T}-V.

$$R_{1}=\frac{5V}{10I_{T}-V}$$

Variable R_{1} cannot be equal to 0.

$$R_{1}=\frac{5V}{10I_{T}-V}\text{, }R_{1}\neq 0$$

Solve for I_T

$$I_{T}=\frac{V\left(R_{1}+5\right)}{10R_{1}}$$

$$R_{1}\neq 0$$