Solve 1/3S=1/2xy

$$\frac { 1 } { 3 } S = \frac { 1 } { 2 } x y$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

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

$$\frac{1}{2}xy=\frac{1}{3}S$$

The equation is in standard form.

$$\frac{y}{2}x=\frac{S}{3}$$

Divide both sides by \frac{1}{2}y.

$$\frac{2\times \frac{y}{2}x}{y}=\frac{S}{3\times \frac{y}{2}}$$

Dividing by \frac{1}{2}y undoes the multiplication by \frac{1}{2}y.

$$x=\frac{S}{3\times \frac{y}{2}}$$

Divide \frac{S}{3} by \frac{1}{2}y.

$$x=\frac{2S}{3y}$$

Solve for S

$$S=\frac{3xy}{2}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{3}S=\frac{xy}{2}$$

Multiply both sides by 3.

$$\frac{\frac{1}{3}S}{\frac{1}{3}}=\frac{xy}{\frac{1}{3}\times 2}$$

Dividing by \frac{1}{3} undoes the multiplication by \frac{1}{3}.

$$S=\frac{xy}{\frac{1}{3}\times 2}$$

Divide \frac{xy}{2} by \frac{1}{3} by multiplying \frac{xy}{2} by the reciprocal of \frac{1}{3}.

$$S=\frac{3xy}{2}$$

Solve for x

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

Steps for Solving Linear Equation

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

$$\frac{1}{2}xy=\frac{1}{3}S$$

The equation is in standard form.

$$\frac{y}{2}x=\frac{S}{3}$$

Divide both sides by \frac{1}{2}y.

$$\frac{2\times \frac{y}{2}x}{y}=\frac{S}{3\times \frac{y}{2}}$$

Dividing by \frac{1}{2}y undoes the multiplication by \frac{1}{2}y.

$$x=\frac{S}{3\times \frac{y}{2}}$$

Divide \frac{S}{3} by \frac{1}{2}y.

$$x=\frac{2S}{3y}$$