Solve {l}{1/2{(x-1)}-0*4{(x-6)}=0}{y=5}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{1}{2} {(x - 1)} - 0 \cdot 4 {(x - 6)} = 0 }\\ { y = 5 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=5$$

Solution Steps

Consider the first equation. Use the distributive property to multiply \frac{1}{2} by x-1.

$$\frac{1}{2}x-\frac{1}{2}-0\times 4\left(x-6\right)=0$$

Multiply 0 and 4 to get 0.

$$\frac{1}{2}x-\frac{1}{2}-0\left(x-6\right)=0$$

Anything times zero gives zero.

$$\frac{1}{2}x-\frac{1}{2}-0=0$$

Add 0 to both sides.

$$\frac{1}{2}x-\frac{1}{2}=0+0$$

Add 0 and 0 to get 0.

$$\frac{1}{2}x-\frac{1}{2}=0$$

Add \frac{1}{2} to both sides. Anything plus zero gives itself.

$$\frac{1}{2}x=\frac{1}{2}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x=\frac{1}{2}\times 2$$

Multiply \frac{1}{2} and 2 to get 1.

$$x=1$$

The system is now solved.

$$x=1 y=5 z=5$$