Solve {l}{pi{(x)}=2}{y=5*x-5}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \pi {(x)} = 2 }\\ { y = 5 \cdot x - 5 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=\frac{10}{\pi }-5\approx -1.816901138$$

Short Steps Using Substitution

Reorder the equations.

$$y=5x-5 \pi x=2 z=y$$

Substitute -5+5x for y in the equation z=y.

$$z=-5+5x$$

Solve \pi x=2 for x.

$$x=2\pi ^{-1}$$

Substitute 2\pi ^{-1} for x in the equation z=-5+5x.

$$z=-5+5\times 2\pi ^{-1}$$

Calculate z from z=-5+5\times 2\pi ^{-1}.

$$z=10\pi ^{-1}-5$$

Substitute 2\pi ^{-1} for x in the equation y=5x-5.

$$y=5\times 2\pi ^{-1}-5$$

Calculate y from y=5\times 2\pi ^{-1}-5.

$$y=10\pi ^{-1}-5$$

The system is now solved.

$$x=2\pi ^{-1} y=10\pi ^{-1}-5 z=10\pi ^{-1}-5$$