Solve {l}{1.2x-y+3z=-2}{2quadx+4y-2z=-3}{3.3x+24+2z=-3}

$$\left. \begin{array} { l } { 1.2 x - y + 3 z = - 2 } \\ { 2 \quad x + 4 y - 2 z = - 3 } \\ { 3.3 x + 24 + 2 z = - 3 } \end{array} \right.$$

Solve for x, y, z

$$x = -\frac{1240}{97} = -12\frac{76}{97} \approx -12.783505155$$

$$y = \frac{1831}{194} = 9\frac{85}{194} \approx 9.43814433$$

$$z = \frac{1473}{194} = 7\frac{115}{194} \approx 7.592783505$$

Short Steps Using Substitution

Solve 1.2x-y+3z=-2 for y.

$$y=1.2x+3z+2$$

Substitute 1.2x+3z+2 for y in the equation 2x+4y-2z=-3.

$$2x+4\left(1.2x+3z+2\right)-2z=-3$$

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

$$x=-\frac{25}{17}z-\frac{55}{34} z=-\frac{33}{20}x-\frac{27}{2}$$

Substitute -\frac{25}{17}z-\frac{55}{34} for x in the equation z=-\frac{33}{20}x-\frac{27}{2}.

$$z=-\frac{33}{20}\left(-\frac{25}{17}z-\frac{55}{34}\right)-\frac{27}{2}$$

Solve z=-\frac{33}{20}\left(-\frac{25}{17}z-\frac{55}{34}\right)-\frac{27}{2} for z.

$$z=\frac{1473}{194}$$

Substitute \frac{1473}{194} for z in the equation x=-\frac{25}{17}z-\frac{55}{34}.

$$x=-\frac{25}{17}\times \frac{1473}{194}-\frac{55}{34}$$

Calculate x from x=-\frac{25}{17}\times \frac{1473}{194}-\frac{55}{34}.

$$x=-\frac{1240}{97}$$

Substitute -\frac{1240}{97} for x and \frac{1473}{194} for z in the equation y=1.2x+3z+2.

$$y=1.2\left(-\frac{1240}{97}\right)+3\times \frac{1473}{194}+2$$

Calculate y from y=1.2\left(-\frac{1240}{97}\right)+3\times \frac{1473}{194}+2.

$$y=\frac{1831}{194}$$

The system is now solved.

$$x=-\frac{1240}{97} y=\frac{1831}{194} z=\frac{1473}{194}$$