Solve mathscr{Y}*s/3+t/2=6

$$\mathscr { Y } \cdot \frac { s } { 3 } + \frac { t } { 2 } = 6$$

Solve for Y

$$\left\{\begin{matrix}Y=-\frac{3\left(t-12\right)}{2s}\text{, }&s\neq 0\\Y\in \mathrm{R}\text{, }&t=12\text{ and }s=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2Ys+3t=36$$

Subtract 3t from both sides.

$$2Ys=36-3t$$

The equation is in standard form.

$$2sY=36-3t$$

Divide both sides by 2s.

$$\frac{2sY}{2s}=\frac{36-3t}{2s}$$

Dividing by 2s undoes the multiplication by 2s.

$$Y=\frac{36-3t}{2s}$$

Divide 36-3t by 2s.

$$Y=\frac{3\left(12-t\right)}{2s}$$

Solve for s

$$\left\{\begin{matrix}s=-\frac{3\left(t-12\right)}{2Y}\text{, }&Y\neq 0\\s\in \mathrm{R}\text{, }&t=12\text{ and }Y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2Ys+3t=36$$

Subtract 3t from both sides.

$$2Ys=36-3t$$

Divide both sides by 2Y.

$$\frac{2Ys}{2Y}=\frac{36-3t}{2Y}$$

Dividing by 2Y undoes the multiplication by 2Y.

$$s=\frac{36-3t}{2Y}$$

Divide 36-3t by 2Y.

$$s=\frac{3\left(12-t\right)}{2Y}$$