Solve 1/3xy+3z=2/4s

$$\frac { 1 } { 3 } x y + 3 z = \frac { 2 } { 4 } s$$

Solve for s

$$s=\frac{2\left(xy+9z\right)}{3}$$

Steps for Solving Linear Equation

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}xy+3z=\frac{1}{2}s$$

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

$$\frac{1}{2}s=\frac{1}{3}xy+3z$$

The equation is in standard form.

$$\frac{1}{2}s=\frac{xy}{3}+3z$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}s}{\frac{1}{2}}=\frac{\frac{xy}{3}+3z}{\frac{1}{2}}$$

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

$$s=\frac{\frac{xy}{3}+3z}{\frac{1}{2}}$$

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

$$s=\frac{2xy}{3}+6z$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{3\left(6z-s\right)}{2y}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&z=\frac{s}{6}\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{3}xy+3z=\frac{1}{2}s$$

Subtract 3z from both sides.

$$\frac{1}{3}xy=\frac{1}{2}s-3z$$

The equation is in standard form.

$$\frac{y}{3}x=\frac{s}{2}-3z$$

Divide both sides by \frac{1}{3}y.

$$\frac{3\times \frac{y}{3}x}{y}=\frac{3\left(\frac{s}{2}-3z\right)}{y}$$

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

$$x=\frac{3\left(\frac{s}{2}-3z\right)}{y}$$

Divide \frac{s}{2}-3z by \frac{1}{3}y.

$$x=\frac{3\left(s-6z\right)}{2y}$$