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

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

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{2}-1 by x.

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

Add y to both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by \sqrt{2}-1.

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

Dividing by \sqrt{2}-1 undoes the multiplication by \sqrt{2}-1.

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

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

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

Solve for y

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

Steps for Solving Linear Equation

Use the distributive property to multiply \sqrt{2}-1 by x.

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

Subtract \sqrt{2}x from both sides.

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

Add x to both sides.

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

Reorder the terms.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide -\sqrt{2}x+x+\sqrt{2} by -1.

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