Solve {l}{x+2y-3z=50}{2x+y+2z=3}{2x-5y+4z=-79}

$$\left. \begin{array} { l } { x + 2 y - 3 z = 50 } \\ { 2 x + y + 2 z = 3 } \\ { 2 x - 5 y + 4 z = - 79 } \end{array} \right.$$

Solve for x, y, z

$$x=4$$

$$y=11$$

$$z=-8$$

Short Steps Using Substitution

Solve x+2y-3z=50 for x.

$$x=-2y+3z+50$$

Substitute -2y+3z+50 for x in the second and third equation.

$$2\left(-2y+3z+50\right)+y+2z=3 2\left(-2y+3z+50\right)-5y+4z=-79$$

Solve these equations for y and z respectively.

$$y=\frac{8}{3}z+\frac{97}{3} z=\frac{9}{10}y-\frac{179}{10}$$

Substitute \frac{8}{3}z+\frac{97}{3} for y in the equation z=\frac{9}{10}y-\frac{179}{10}.

$$z=\frac{9}{10}\left(\frac{8}{3}z+\frac{97}{3}\right)-\frac{179}{10}$$

Solve z=\frac{9}{10}\left(\frac{8}{3}z+\frac{97}{3}\right)-\frac{179}{10} for z.

$$z=-8$$

Substitute -8 for z in the equation y=\frac{8}{3}z+\frac{97}{3}.

$$y=\frac{8}{3}\left(-8\right)+\frac{97}{3}$$

Calculate y from y=\frac{8}{3}\left(-8\right)+\frac{97}{3}.

$$y=11$$

Substitute 11 for y and -8 for z in the equation x=-2y+3z+50.

$$x=-2\times 11+3\left(-8\right)+50$$

Calculate x from x=-2\times 11+3\left(-8\right)+50.

$$x=4$$

The system is now solved.

$$x=4 y=11 z=-8$$