Solve {l}{3x=4}{y=7x-4}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 3 x = 4 }\\ { y = 7 x - 4 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{16}{3} = 5\frac{1}{3} \approx 5.333333333$$

Solution Steps

Consider the first equation. Divide both sides by 3.

$$x=\frac{4}{3}$$

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

$$y=7\times \frac{4}{3}-4$$

Multiply 7 and \frac{4}{3} to get \frac{28}{3}.

$$y=\frac{28}{3}-4$$

Subtract 4 from \frac{28}{3} to get \frac{16}{3}.

$$y=\frac{16}{3}$$

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

$$z=\frac{16}{3}$$

The system is now solved.

$$x=\frac{4}{3} y=\frac{16}{3} z=\frac{16}{3}$$