Solve {l}{7{(x-1)}=4}{y=5x-1}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 7 {(x - 1)} = 4 }\\ { y = 5 x - 1 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z = \frac{48}{7} = 6\frac{6}{7} \approx 6.857142857$$

Solution Steps

Consider the first equation. Divide both sides by 7.

$$x-1=\frac{4}{7}$$

Add 1 to both sides.

$$x=\frac{4}{7}+1$$

Add \frac{4}{7} and 1 to get \frac{11}{7}.

$$x=\frac{11}{7}$$

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

$$y=5\times \frac{11}{7}-1$$

Multiply 5 and \frac{11}{7} to get \frac{55}{7}.

$$y=\frac{55}{7}-1$$

Subtract 1 from \frac{55}{7} to get \frac{48}{7}.

$$y=\frac{48}{7}$$

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

$$z=\frac{48}{7}$$

The system is now solved.

$$x=\frac{11}{7} y=\frac{48}{7} z=\frac{48}{7}$$