Solve 1000x/y=1000-x

$$\frac { 1000 x } { y } = 1000 - x$$

Solve for x

$$x=\frac{1000y}{y+1000}$$

$$y\neq -1000\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$1000x=y\times 1000-xy$$

Add xy to both sides.

$$1000x+xy=y\times 1000$$

Combine all terms containing x.

$$\left(1000+y\right)x=y\times 1000$$

The equation is in standard form.

$$\left(y+1000\right)x=1000y$$

Divide both sides by y+1000.

$$\frac{\left(y+1000\right)x}{y+1000}=\frac{1000y}{y+1000}$$

Dividing by y+1000 undoes the multiplication by y+1000.

$$x=\frac{1000y}{y+1000}$$

Solve for y

$$y=-\frac{1000x}{x-1000}$$

$$x\neq 0\text{ and }x\neq 1000$$

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 y.

$$1000x=y\times 1000-xy$$

Swap sides so that all variable terms are on the left hand side.

$$y\times 1000-xy=1000x$$

Combine all terms containing y.

$$\left(1000-x\right)y=1000x$$

Divide both sides by 1000-x.

$$\frac{\left(1000-x\right)y}{1000-x}=\frac{1000x}{1000-x}$$

Dividing by 1000-x undoes the multiplication by 1000-x.

$$y=\frac{1000x}{1000-x}$$

Variable y cannot be equal to 0.

$$y=\frac{1000x}{1000-x}\text{, }y\neq 0$$