Solve y=sqrt{2}x-2sqrt{2}-1

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

Solve for x

$$x=\frac{\sqrt{2}y+\sqrt{2}+4}{2}$$

Steps for Solving Linear Equation

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

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

Add 2\sqrt{2} to both sides.

$$\sqrt{2}x-1=y+2\sqrt{2}$$

Add 1 to both sides.

$$\sqrt{2}x=y+2\sqrt{2}+1$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}x}{\sqrt{2}}=\frac{y+2\sqrt{2}+1}{\sqrt{2}}$$

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

$$x=\frac{y+2\sqrt{2}+1}{\sqrt{2}}$$

Divide y+2\sqrt{2}+1 by \sqrt{2}.

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

Solve for y

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