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

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

Solve for x, y, z

$$x=\frac{1}{13}\approx 0.076923077$$

$$y = \frac{41}{13} = 3\frac{2}{13} \approx 3.153846154$$

$$z=-\frac{8}{13}\approx -0.615384615$$

Short Steps Using Substitution

Solve 3x+y-z=4 for y.

$$y=-3x+z+4$$

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

$$-3x+z+4-2x=3$$

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

$$x=\frac{3}{2}z+1 z=5x-1$$

Substitute \frac{3}{2}z+1 for x in the equation z=5x-1.

$$z=5\left(\frac{3}{2}z+1\right)-1$$

Solve z=5\left(\frac{3}{2}z+1\right)-1 for z.

$$z=-\frac{8}{13}$$

Substitute -\frac{8}{13} for z in the equation x=\frac{3}{2}z+1.

$$x=\frac{3}{2}\left(-\frac{8}{13}\right)+1$$

Calculate x from x=\frac{3}{2}\left(-\frac{8}{13}\right)+1.

$$x=\frac{1}{13}$$

Substitute \frac{1}{13} for x and -\frac{8}{13} for z in the equation y=-3x+z+4.

$$y=-3\times \frac{1}{13}-\frac{8}{13}+4$$

Calculate y from y=-3\times \frac{1}{13}-\frac{8}{13}+4.

$$y=\frac{41}{13}$$

The system is now solved.

$$x=\frac{1}{13} y=\frac{41}{13} z=-\frac{8}{13}$$