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

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

Solve for x, y, z

$$z=0$$

Solution Steps

Consider the first equation. Multiply 2 and 5 to get 10.

$$6+10x-\frac{1}{6}=\frac{1}{2}$$

Subtract \frac{1}{6} from 6 to get \frac{35}{6}.

$$\frac{35}{6}+10x=\frac{1}{2}$$

Subtract \frac{35}{6} from both sides.

$$10x=\frac{1}{2}-\frac{35}{6}$$

Subtract \frac{35}{6} from \frac{1}{2} to get -\frac{16}{3}.

$$10x=-\frac{16}{3}$$

Divide both sides by 10.

$$x=\frac{-\frac{16}{3}}{10}$$

Express \frac{-\frac{16}{3}}{10} as a single fraction.

$$x=\frac{-16}{3\times 10}$$

Multiply 3 and 10 to get 30.

$$x=\frac{-16}{30}$$

Reduce the fraction \frac{-16}{30} to lowest terms by extracting and canceling out 2.

$$x=-\frac{8}{15}$$

The system is now solved.

$$x=-\frac{8}{15} y=0 z=0$$