Solve {l}{1/x+1/y=1}{text{tindgraph}}

$$\left. \begin{array} { l } { \frac { 1 } { x } + \frac { 1 } { y } = 1 } \\ { \text { tind graph } } \end{array} \right.$$

Solve for x

$$x=-\frac{y}{1-y}$$

$$y\neq 0\text{ and }y\neq 1$$

Steps for Solving Linear Equation

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

$$y+x=xy$$

Subtract xy from both sides.

$$y+x-xy=0$$

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

$$x-xy=-y$$

Combine all terms containing x.

$$\left(1-y\right)x=-y$$

Divide both sides by 1-y.

$$\frac{\left(1-y\right)x}{1-y}=-\frac{y}{1-y}$$

Dividing by 1-y undoes the multiplication by 1-y.

$$x=-\frac{y}{1-y}$$

Variable x cannot be equal to 0.

$$x=-\frac{y}{1-y}\text{, }x\neq 0$$