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

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

Solve for y

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

Steps for Solving Linear Equation

Multiply -1 and 2 to get -2.

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

Subtract x from both sides.

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

The equation is in standard form.

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

Divide both sides by -2\sqrt{2}.

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

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

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

Divide \sqrt{2}-x by -2\sqrt{2}.

$$y=\frac{\sqrt{2}x}{4}-\frac{1}{2}$$

Solve for x

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

Solution Steps

Add 2\sqrt{2}y to both sides.

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