Solve {l}{2y=frac{sqrt{3x}}{2}-1}{x=3}{z=y}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { 2 y = \frac{\sqrt{3 x}}{2} - 1 }\\ { x = 3 }\\ { z = y }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for y, x, z, a

$$a=\frac{1}{4}=0.25$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$2y=\frac{\sqrt{3\times 3}}{2}-1$$

Multiply both sides of the equation by 2.

$$4y=\sqrt{3\times 3}-2$$

Multiply 3 and 3 to get 9.

$$4y=\sqrt{9}-2$$

Calculate the square root of 9 and get 3.

$$4y=3-2$$

Subtract 2 from 3 to get 1.

$$4y=1$$

Divide both sides by 4.

$$y=\frac{1}{4}$$

Consider the third equation. Insert the known values of variables into the equation.

$$z=\frac{1}{4}$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$a=\frac{1}{4}$$

The system is now solved.

$$y=\frac{1}{4} x=3 z=\frac{1}{4} a=\frac{1}{4}$$