Solve {l}{x-3y=8}{y+6z=1}{-z+4x=3}

$$\left\{ \begin{array} { l } { x - 3 y = 8 } \\ { y + 6 z = 1 } \\ { - z + 4 x = 3 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{65}{73}\approx 0.890410959$$

$$y = -\frac{173}{73} = -2\frac{27}{73} \approx -2.369863014$$

$$z=\frac{41}{73}\approx 0.561643836$$

Short Steps Using Substitution

Solve x-3y=8 for x.

$$x=3y+8$$

Substitute 3y+8 for x in the equation -z+4x=3.

$$-z+4\left(3y+8\right)=3$$

Solve the second equation for y and the third equation for z.

$$y=-6z+1 z=12y+29$$

Substitute -6z+1 for y in the equation z=12y+29.

$$z=12\left(-6z+1\right)+29$$

Solve z=12\left(-6z+1\right)+29 for z.

$$z=\frac{41}{73}$$

Substitute \frac{41}{73} for z in the equation y=-6z+1.

$$y=-6\times \frac{41}{73}+1$$

Calculate y from y=-6\times \frac{41}{73}+1.

$$y=-\frac{173}{73}$$

Substitute -\frac{173}{73} for y in the equation x=3y+8.

$$x=3\left(-\frac{173}{73}\right)+8$$

Calculate x from x=3\left(-\frac{173}{73}\right)+8.

$$x=\frac{65}{73}$$

The system is now solved.

$$x=\frac{65}{73} y=-\frac{173}{73} z=\frac{41}{73}$$