Solve {l}{y=x}{z={(pi/2-x)}}{text{Solvefor}atext{where}}{a=z}

$$\left. \begin{array} { l } { y = x }\\ { z = {(\frac{\pi}{2} - x)} }\\ { \text{Solve for } a \text{ where} } \\ { a = z } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{\pi -2a}{2}$$

$$y=\frac{\pi -2a}{2}$$

$$z=a$$

Short Steps Using Substitution

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

$$y=x 2z=\pi -2x a=z$$

Solve the second equation for x and the third equation for z.

$$x=-z+\frac{1}{2}\pi z=a$$

Substitute a for z in the equation x=-z+\frac{1}{2}\pi .

$$x=-a+\frac{1}{2}\pi$$

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

$$y=\frac{1}{2}\pi -a$$

The system is now solved.

$$x=-a+\frac{1}{2}\pi y=\frac{1}{2}\pi -a z=a$$