Solve {l}{5x=6/5}{y=3x+6}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 5 x = \frac{6}{5} }\\ { y = 3 x + 6 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{168}{25} = 6\frac{18}{25} = 6.72$$

Solution Steps

Consider the first equation. Divide both sides by 5.

$$x=\frac{\frac{6}{5}}{5}$$

Express \frac{\frac{6}{5}}{5} as a single fraction.

$$x=\frac{6}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$x=\frac{6}{25}$$

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

$$y=3\times \frac{6}{25}+6$$

Multiply 3 and \frac{6}{25} to get \frac{18}{25}.

$$y=\frac{18}{25}+6$$

Add \frac{18}{25} and 6 to get \frac{168}{25}.

$$y=\frac{168}{25}$$

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

$$z=\frac{168}{25}$$

The system is now solved.

$$x=\frac{6}{25} y=\frac{168}{25} z=\frac{168}{25}$$