Solve z=4-x^2-y

$$z = 4 - x ^ { 2 } - y$$

Solve for y

$$y=4-z-x^{2}$$

Steps for Solving Linear Equation

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

$$4-x^{2}-y=z$$

Subtract 4 from both sides.

$$-x^{2}-y=z-4$$

Add x^{2} to both sides.

$$-y=z-4+x^{2}$$

The equation is in standard form.

$$-y=x^{2}+z-4$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{x^{2}+z-4}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{x^{2}+z-4}{-1}$$

Divide z-4+x^{2} by -1.

$$y=4-z-x^{2}$$

Solve for x

$$x=\sqrt{4-z-y}$$

$$x=-\sqrt{4-z-y}\text{, }z\leq 4-y$$