Solve {l}{2x=3pi/6pi}{y=x}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 2 x = \frac{3 \pi}{6} \pi }\\ { y = x }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{\pi ^ {2}}{4} \approx 2.4674011$$

Short Steps Using Substitution

Multiply each equation by the least common multiple of denominators in it. Simplify.

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

Substitute \frac{1}{4}\pi ^{2} for x in the equation y=x.

$$y=\frac{1}{4}\pi ^{2}$$

Solve z=y for z.

$$z=y$$

Substitute \frac{1}{4}\pi ^{2} for y in the equation z=y.

$$z=\frac{1}{4}\pi ^{2}$$

The system is now solved.

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