Solve 1/x+2/y=1

$$\frac { 1 } { x } + \frac { 2 } { y } = 1$$

Solve for x

$$x=-\frac{y}{2-y}$$

$$y\neq 0\text{ and }y\neq 2$$

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.

$$y+x\times 2=xy$$

Subtract xy from both sides.

$$y+x\times 2-xy=0$$

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

$$x\times 2-xy=-y$$

Combine all terms containing x.

$$\left(2-y\right)x=-y$$

Divide both sides by 2-y.

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

Dividing by 2-y undoes the multiplication by 2-y.

$$x=-\frac{y}{2-y}$$

Variable x cannot be equal to 0.

$$x=-\frac{y}{2-y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{2x}{1-x}$$

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

Steps for Solving Linear Equation

Variable y 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.

$$y+x\times 2=xy$$

Subtract xy from both sides.

$$y+x\times 2-xy=0$$

Subtract x\times 2 from both sides. Anything subtracted from zero gives its negation.

$$y-xy=-x\times 2$$

Multiply -1 and 2 to get -2.

$$y-xy=-2x$$

Combine all terms containing y.

$$\left(1-x\right)y=-2x$$

Divide both sides by 1-x.

$$\frac{\left(1-x\right)y}{1-x}=-\frac{2x}{1-x}$$

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

$$y=-\frac{2x}{1-x}$$

Variable y cannot be equal to 0.

$$y=-\frac{2x}{1-x}\text{, }y\neq 0$$