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

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

Solve for x

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

Steps for Solving Linear Equation

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

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

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

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

Subtract \sqrt{2}y from both sides.

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

Add y to both sides.

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

Reorder the terms.

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

Combine all terms containing x.

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

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

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

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

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

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

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

Solve for y

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

Steps for Solving Linear Equation

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

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

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

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

Subtract \sqrt{2}x from both sides.

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

Add 2x to both sides.

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

Reorder the terms.

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

Combine all terms containing y.

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

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

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

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

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

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

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