Solve y=-2x/x-6+1

$$y = \frac { - 2 x } { x - 6 } + 1$$

Solve for x

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

$$y\neq -1$$

Steps for Solving Linear Equation

Variable x cannot be equal to 6 since division by zero is not defined. Multiply both sides of the equation by x-6.

$$y\left(x-6\right)=-2x+x-6$$

Use the distributive property to multiply y by x-6.

$$yx-6y=-2x+x-6$$

Combine -2x and x to get -x.

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

Add x to both sides.

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

Add 6y to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y+1.

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

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

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

Divide -6+6y by y+1.

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

Variable x cannot be equal to 6.

$$x=\frac{6\left(y-1\right)}{y+1}\text{, }x\neq 6$$

Solve for y

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

$$x\neq 6$$