Solve {l}{x-2y+z=NL+4}{2x+y-z=2NL-3}{-x+3y+2z=1-NL}

$$\left\{ \begin{array} { l } { x - 2 y + z = N L + 4 } \\ { 2 x + y - z = 2 N L - 3 } \\ { - x + 3 y + 2 z = 1 - N L } \end{array} \right.$$

Solve for x, y, z

$$x=LN$$

$$y=-1$$

$$z=2$$

Short Steps Using Substitution

Solve x-2y+z=NL+4 for x.

$$x=2y-z+LN+4$$

Substitute 2y-z+LN+4 for x in the second and third equation.

$$2\left(2y-z+LN+4\right)+y-z=2NL-3 -\left(2y-z+LN+4\right)+3y+2z=1-NL$$

Solve these equations for y and z respectively.

$$y=\frac{3}{5}z-\frac{11}{5} z=-\frac{1}{3}y+\frac{5}{3}$$

Substitute \frac{3}{5}z-\frac{11}{5} for y in the equation z=-\frac{1}{3}y+\frac{5}{3}.

$$z=-\frac{1}{3}\left(\frac{3}{5}z-\frac{11}{5}\right)+\frac{5}{3}$$

Solve z=-\frac{1}{3}\left(\frac{3}{5}z-\frac{11}{5}\right)+\frac{5}{3} for z.

$$z=2$$

Substitute 2 for z in the equation y=\frac{3}{5}z-\frac{11}{5}.

$$y=\frac{3}{5}\times 2-\frac{11}{5}$$

Calculate y from y=\frac{3}{5}\times 2-\frac{11}{5}.

$$y=-1$$

Substitute -1 for y and 2 for z in the equation x=2y-z+LN+4.

$$x=2\left(-1\right)-2+LN+4$$

Calculate x from x=2\left(-1\right)-2+LN+4.

$$x=NL$$

The system is now solved.

$$x=NL y=-1 z=2$$