Solve {l}{{(3)}+x+1/2=6}{y={(x-1)}^(x-2)}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { {(3)} + \frac{x + 1}{2} = 6 }\\ { y = {(x - 1)} ^ {{(x - 2)}} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=64$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 2.

$$6+x+1=12$$

Add 6 and 1 to get 7.

$$7+x=12$$

Subtract 7 from both sides.

$$x=12-7$$

Subtract 7 from 12 to get 5.

$$x=5$$

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

$$y=\left(5-1\right)^{5-2}$$

Subtract 1 from 5 to get 4.

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

Subtract 2 from 5 to get 3.

$$y=4^{3}$$

Calculate 4 to the power of 3 and get 64.

$$y=64$$

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

$$z=64$$

The system is now solved.

$$x=5 y=64 z=64$$