Solve {l}{x+y-z=-4}{2x+y+z=6}{x+4y-2z=-6}

$$\left. \begin{array} { l } { x + y - z = - 4 } \\ { 2 x + y + z = 6 } \\ { x + 4 y - 2 z = - 6 } \end{array} \right.$$

Solve for x, y, z

$$x=0$$

$$y=1$$

$$z=5$$

Short Steps Using Substitution

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

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

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

$$2\left(-y+z-4\right)+y+z=6 -y+z-4+4y-2z=-6$$

Solve these equations for y and z respectively.

$$y=3z-14 z=3y+2$$

Substitute 3z-14 for y in the equation z=3y+2.

$$z=3\left(3z-14\right)+2$$

Solve z=3\left(3z-14\right)+2 for z.

$$z=5$$

Substitute 5 for z in the equation y=3z-14.

$$y=3\times 5-14$$

Calculate y from y=3\times 5-14.

$$y=1$$

Substitute 1 for y and 5 for z in the equation x=-y+z-4.

$$x=-1+5-4$$

Calculate x from x=-1+5-4.

$$x=0$$

The system is now solved.

$$x=0 y=1 z=5$$