Solve k_{r}f_{1}:y=2x+1

$$k _ { r } f _ { 1 } : y = 2 x + 1$$

Solve for f_1 (complex solution)

$$\left\{\begin{matrix}f_{1}=\frac{y\left(2x+1\right)}{k_{r}}\text{, }&k_{r}\neq 0\text{ and }y\neq 0\\f_{1}\in \mathrm{C}\text{, }&x=-\frac{1}{2}\text{ and }k_{r}=0\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$k_{r}f_{1}=2xy+y$$

Divide both sides by k_{r}.

$$\frac{k_{r}f_{1}}{k_{r}}=\frac{2xy+y}{k_{r}}$$

Dividing by k_{r} undoes the multiplication by k_{r}.

$$f_{1}=\frac{2xy+y}{k_{r}}$$

Divide 2yx+y by k_{r}.

$$f_{1}=\frac{y\left(2x+1\right)}{k_{r}}$$

Solve for k_r (complex solution)

$$\left\{\begin{matrix}k_{r}=\frac{y\left(2x+1\right)}{f_{1}}\text{, }&f_{1}\neq 0\text{ and }y\neq 0\\k_{r}\in \mathrm{C}\text{, }&x=-\frac{1}{2}\text{ and }f_{1}=0\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$k_{r}f_{1}=2xy+y$$

The equation is in standard form.

$$f_{1}k_{r}=2xy+y$$

Divide both sides by f_{1}.

$$\frac{f_{1}k_{r}}{f_{1}}=\frac{2xy+y}{f_{1}}$$

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

$$k_{r}=\frac{2xy+y}{f_{1}}$$

Divide 2yx+y by f_{1}.

$$k_{r}=\frac{y\left(2x+1\right)}{f_{1}}$$

Solve for f_1

$$\left\{\begin{matrix}f_{1}=\frac{y\left(2x+1\right)}{k_{r}}\text{, }&k_{r}\neq 0\text{ and }y\neq 0\\f_{1}\in \mathrm{R}\text{, }&x=-\frac{1}{2}\text{ and }k_{r}=0\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$k_{r}f_{1}=2xy+y$$

Divide both sides by k_{r}.

$$\frac{k_{r}f_{1}}{k_{r}}=\frac{2xy+y}{k_{r}}$$

Dividing by k_{r} undoes the multiplication by k_{r}.

$$f_{1}=\frac{2xy+y}{k_{r}}$$

Divide 2yx+y by k_{r}.

$$f_{1}=\frac{y\left(2x+1\right)}{k_{r}}$$

Solve for k_r

$$\left\{\begin{matrix}k_{r}=\frac{y\left(2x+1\right)}{f_{1}}\text{, }&f_{1}\neq 0\text{ and }y\neq 0\\k_{r}\in \mathrm{R}\text{, }&x=-\frac{1}{2}\text{ and }f_{1}=0\text{ and }y\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$k_{r}f_{1}=2xy+y$$

The equation is in standard form.

$$f_{1}k_{r}=2xy+y$$

Divide both sides by f_{1}.

$$\frac{f_{1}k_{r}}{f_{1}}=\frac{2xy+y}{f_{1}}$$

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

$$k_{r}=\frac{2xy+y}{f_{1}}$$

Divide 2yx+y by f_{1}.

$$k_{r}=\frac{y\left(2x+1\right)}{f_{1}}$$