Solve x=sqrt{1-y}

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

Solve for y

$$y=1-x^{2}$$

$$x\geq 0$$

Steps for Solving Radical Equations

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

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

Square both sides of the equation.

$$-y+1=x^{2}$$

Subtract 1 from both sides of the equation.

$$-y+1-1=x^{2}-1$$

Subtracting 1 from itself leaves 0.

$$-y=x^{2}-1$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{x^{2}-1}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{x^{2}-1}{-1}$$

Divide x^{2}-1 by -1.

$$y=1-x^{2}$$

Solve for y (complex solution)

$$y=1-x^{2}$$

$$arg(x)<\pi \text{ or }x=0$$

Solve for x

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

$$y\leq 1$$