Solve -1/y=x-2

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

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$-1=yx+y\left(-2\right)$$

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

$$yx+y\left(-2\right)=-1$$

Subtract y\left(-2\right) from both sides.

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

Multiply -1 and -2 to get 2.

$$yx=-1+2y$$

The equation is in standard form.

$$yx=2y-1$$

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Divide 2y-1 by y.

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

Solve for y

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

$$x\neq 2$$

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.

$$-1=yx+y\left(-2\right)$$

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

$$yx+y\left(-2\right)=-1$$

Combine all terms containing y.

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

Divide both sides by x-2.

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

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

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

Variable y cannot be equal to 0.

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