Solve x/3+y/n=1

$$\frac { x } { 3 } + \frac { y } { n } = 1$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{3y}{x-3}\text{, }&y\neq 0\text{ and }x\neq 3\\n\neq 0\text{, }&x=3\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3n, the least common multiple of 3,n.

$$nx+3y=3n$$

Subtract 3n from both sides.

$$nx+3y-3n=0$$

Subtract 3y from both sides. Anything subtracted from zero gives its negation.

$$nx-3n=-3y$$

Combine all terms containing n.

$$\left(x-3\right)n=-3y$$

Divide both sides by x-3.

$$\frac{\left(x-3\right)n}{x-3}=-\frac{3y}{x-3}$$

Dividing by x-3 undoes the multiplication by x-3.

$$n=-\frac{3y}{x-3}$$

Variable n cannot be equal to 0.

$$n=-\frac{3y}{x-3}\text{, }n\neq 0$$

Solve for x

$$x=-\frac{3y}{n}+3$$

$$n\neq 0$$

Steps for Solving Linear Equation

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

$$nx+3y=3n$$

Subtract 3y from both sides.

$$nx=3n-3y$$

Divide both sides by n.

$$\frac{nx}{n}=\frac{3n-3y}{n}$$

Dividing by n undoes the multiplication by n.

$$x=\frac{3n-3y}{n}$$

Divide 3n-3y by n.

$$x=-\frac{3y}{n}+3$$