Solve 1000/x-1=y

$$\frac{ 1000 }{ x } -1=y$$

Solve for x

$$x=\frac{1000}{y+1}$$

$$y\neq -1$$

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 x.

$$1000+x\left(-1\right)=yx$$

Subtract yx from both sides.

$$1000+x\left(-1\right)-yx=0$$

Subtract 1000 from both sides. Anything subtracted from zero gives its negation.

$$x\left(-1\right)-yx=-1000$$

Combine all terms containing x.

$$\left(-1-y\right)x=-1000$$

The equation is in standard form.

$$\left(-y-1\right)x=-1000$$

Divide both sides by -1-y.

$$\frac{\left(-y-1\right)x}{-y-1}=-\frac{1000}{-y-1}$$

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

$$x=-\frac{1000}{-y-1}$$

Divide -1000 by -1-y.

$$x=\frac{1000}{y+1}$$

Variable x cannot be equal to 0.

$$x=\frac{1000}{y+1}\text{, }x\neq 0$$

Solve for y

$$y=-1+\frac{1000}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$1000+x\left(-1\right)=yx$$

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

$$yx=1000+x\left(-1\right)$$

The equation is in standard form.

$$xy=1000-x$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide 1000-x by x.

$$y=-1+\frac{1000}{x}$$