Solve y=3k0s1/2x

$$y = 3 k 0 s \frac { 1 } { 2 } x$$

Solve for k_0 (complex solution)

$$\left\{\begin{matrix}k_{0}=\frac{2y}{3sx}\text{, }&x\neq 0\text{ and }s\neq 0\\k_{0}\in \mathrm{C}\text{, }&\left(s=0\text{ or }x=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$y=\frac{3}{2}k_{0}sx$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{3}{2}k_{0}sx=y$$

The equation is in standard form.

$$\frac{3sx}{2}k_{0}=y$$

Divide both sides by \frac{3}{2}sx.

$$\frac{2\times \frac{3sx}{2}k_{0}}{3sx}=\frac{2y}{3sx}$$

Dividing by \frac{3}{2}sx undoes the multiplication by \frac{3}{2}sx.

$$k_{0}=\frac{2y}{3sx}$$

Solve for s (complex solution)

$$\left\{\begin{matrix}s=\frac{2y}{3k_{0}x}\text{, }&x\neq 0\text{ and }k_{0}\neq 0\\s\in \mathrm{C}\text{, }&\left(k_{0}=0\text{ or }x=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$y=\frac{3}{2}k_{0}sx$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{3}{2}k_{0}sx=y$$

The equation is in standard form.

$$\frac{3k_{0}x}{2}s=y$$

Divide both sides by \frac{3}{2}k_{0}x.

$$\frac{2\times \frac{3k_{0}x}{2}s}{3k_{0}x}=\frac{2y}{3k_{0}x}$$

Dividing by \frac{3}{2}k_{0}x undoes the multiplication by \frac{3}{2}k_{0}x.

$$s=\frac{2y}{3k_{0}x}$$

Solve for k_0

$$\left\{\begin{matrix}k_{0}=\frac{2y}{3sx}\text{, }&x\neq 0\text{ and }s\neq 0\\k_{0}\in \mathrm{R}\text{, }&\left(s=0\text{ or }x=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$y=\frac{3}{2}k_{0}sx$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{3}{2}k_{0}sx=y$$

The equation is in standard form.

$$\frac{3sx}{2}k_{0}=y$$

Divide both sides by \frac{3}{2}sx.

$$\frac{2\times \frac{3sx}{2}k_{0}}{3sx}=\frac{2y}{3sx}$$

Dividing by \frac{3}{2}sx undoes the multiplication by \frac{3}{2}sx.

$$k_{0}=\frac{2y}{3sx}$$

Solve for s

$$\left\{\begin{matrix}s=\frac{2y}{3k_{0}x}\text{, }&x\neq 0\text{ and }k_{0}\neq 0\\s\in \mathrm{R}\text{, }&\left(k_{0}=0\text{ or }x=0\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$y=\frac{3}{2}k_{0}sx$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{3}{2}k_{0}sx=y$$

The equation is in standard form.

$$\frac{3k_{0}x}{2}s=y$$

Divide both sides by \frac{3}{2}k_{0}x.

$$\frac{2\times \frac{3k_{0}x}{2}s}{3k_{0}x}=\frac{2y}{3k_{0}x}$$

Dividing by \frac{3}{2}k_{0}x undoes the multiplication by \frac{3}{2}k_{0}x.

$$s=\frac{2y}{3k_{0}x}$$