Solve y=x-6/x-3

$$y = \frac { x - 6 } { x - 3 }$$

Solve for x

$$x=-\frac{3\left(2-y\right)}{y-1}$$

$$y\neq 1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

$$y\left(x-3\right)=x-6$$

Use the distributive property to multiply y by x-3.

$$yx-3y=x-6$$

Subtract x from both sides.

$$yx-3y-x=-6$$

Add 3y to both sides.

$$yx-x=-6+3y$$

Combine all terms containing x.

$$\left(y-1\right)x=-6+3y$$

The equation is in standard form.

$$\left(y-1\right)x=3y-6$$

Divide both sides by y-1.

$$\frac{\left(y-1\right)x}{y-1}=\frac{3y-6}{y-1}$$

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

$$x=\frac{3y-6}{y-1}$$

Divide -6+3y by y-1.

$$x=\frac{3\left(y-2\right)}{y-1}$$

Variable x cannot be equal to 3.

$$x=\frac{3\left(y-2\right)}{y-1}\text{, }x\neq 3$$

Solve for y

$$y=-\frac{6-x}{x-3}$$

$$x\neq 3$$