Solve 2y=sqrt{5-2z}

$$2y= \sqrt{ 5-2z }$$

Solve for y

$$y=\frac{\sqrt{5-2z}}{2}$$

$$z\leq \frac{5}{2}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$2y=\sqrt{5-2z}$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{\sqrt{5-2z}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{\sqrt{5-2z}}{2}$$

Solve for z

$$z=\frac{5}{2}-2y^{2}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{5-2z}=2y$$

Square both sides of the equation.

$$-2z+5=4y^{2}$$

Subtract 5 from both sides of the equation.

$$-2z+5-5=4y^{2}-5$$

Subtracting 5 from itself leaves 0.

$$-2z=4y^{2}-5$$

Divide both sides by -2.

$$\frac{-2z}{-2}=\frac{4y^{2}-5}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$z=\frac{4y^{2}-5}{-2}$$

Divide 4y^{2}-5 by -2.

$$z=\frac{5}{2}-2y^{2}$$