Solve 1/x+1/y=1/2020

$$\frac { 1 } { x } + \frac { 1 } { y } = \frac { 1 } { 2020 }$$

Solve for x

$$x=-\frac{2020y}{2020-y}$$

$$y\neq 0\text{ and }y\neq 2020$$

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 2020xy, the least common multiple of x,y,2020.

$$2020y+2020x=xy$$

Subtract xy from both sides.

$$2020y+2020x-xy=0$$

Subtract 2020y from both sides. Anything subtracted from zero gives its negation.

$$2020x-xy=-2020y$$

Combine all terms containing x.

$$\left(2020-y\right)x=-2020y$$

Divide both sides by 2020-y.

$$\frac{\left(2020-y\right)x}{2020-y}=-\frac{2020y}{2020-y}$$

Dividing by 2020-y undoes the multiplication by 2020-y.

$$x=-\frac{2020y}{2020-y}$$

Variable x cannot be equal to 0.

$$x=-\frac{2020y}{2020-y}\text{, }x\neq 0$$

Solve for y

$$y=-\frac{2020x}{2020-x}$$

$$x\neq 0\text{ and }x\neq 2020$$

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 2020xy, the least common multiple of x,y,2020.

$$2020y+2020x=xy$$

Subtract xy from both sides.

$$2020y+2020x-xy=0$$

Subtract 2020x from both sides. Anything subtracted from zero gives its negation.

$$2020y-xy=-2020x$$

Combine all terms containing y.

$$\left(2020-x\right)y=-2020x$$

Divide both sides by 2020-x.

$$\frac{\left(2020-x\right)y}{2020-x}=-\frac{2020x}{2020-x}$$

Dividing by 2020-x undoes the multiplication by 2020-x.

$$y=-\frac{2020x}{2020-x}$$

Variable y cannot be equal to 0.

$$y=-\frac{2020x}{2020-x}\text{, }y\neq 0$$