Solve {l}{x+2y+7z=17}{18x+7y+z=8}{2x+y+z=5}

$$\left\{ \begin{array} { l } { x + 2 y + 7 z = 17 } \\ { 18 x + 7 y + z = 8 } \\ { 2 x + y + z = 5 } \end{array} \right.$$

Solve for x, y, z

$$x = -\frac{93}{2} = -46\frac{1}{2} = -46.5$$

$$y = \frac{249}{2} = 124\frac{1}{2} = 124.5$$

$$z = -\frac{53}{2} = -26\frac{1}{2} = -26.5$$

Short Steps Using Substitution

Solve x+2y+7z=17 for x.

$$x=-2y-7z+17$$

Substitute -2y-7z+17 for x in the second and third equation.

$$18\left(-2y-7z+17\right)+7y+z=8 2\left(-2y-7z+17\right)+y+z=5$$

Solve these equations for y and z respectively.

$$y=-\frac{125}{29}z+\frac{298}{29} z=-\frac{3}{13}y+\frac{29}{13}$$

Substitute -\frac{125}{29}z+\frac{298}{29} for y in the equation z=-\frac{3}{13}y+\frac{29}{13}.

$$z=-\frac{3}{13}\left(-\frac{125}{29}z+\frac{298}{29}\right)+\frac{29}{13}$$

Solve z=-\frac{3}{13}\left(-\frac{125}{29}z+\frac{298}{29}\right)+\frac{29}{13} for z.

$$z=-\frac{53}{2}$$

Substitute -\frac{53}{2} for z in the equation y=-\frac{125}{29}z+\frac{298}{29}.

$$y=-\frac{125}{29}\left(-\frac{53}{2}\right)+\frac{298}{29}$$

Calculate y from y=-\frac{125}{29}\left(-\frac{53}{2}\right)+\frac{298}{29}.

$$y=\frac{249}{2}$$

Substitute \frac{249}{2} for y and -\frac{53}{2} for z in the equation x=-2y-7z+17.

$$x=-2\times \frac{249}{2}-7\left(-\frac{53}{2}\right)+17$$

Calculate x from x=-2\times \frac{249}{2}-7\left(-\frac{53}{2}\right)+17.

$$x=-\frac{93}{2}$$

The system is now solved.

$$x=-\frac{93}{2} y=\frac{249}{2} z=-\frac{53}{2}$$