Solve {l}{x+y+z-6=0}{x-y+z-2=0}{x-y-z+4=0}

$$\left. \begin{array} { l } { x + y + z - 6 = 0 } \\ { x - y + z - 2 = 0 } \\ { x - y - z + 4 = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=1$$

$$y=2$$

$$z=3$$

Short Steps Using Substitution

Solve x+y+z-6=0 for x.

$$x=-y-z+6$$

Substitute -y-z+6 for x in the second and third equation.

$$-y-z+6-y+z-2=0 -y-z+6-y-z+4=0$$

Solve these equations for y and z respectively.

$$y=2 z=5-y$$

Substitute 2 for y in the equation z=5-y.

$$z=5-2$$

Calculate z from z=5-2.

$$z=3$$

Substitute 2 for y and 3 for z in the equation x=-y-z+6.

$$x=-2-3+6$$

Calculate x from x=-2-3+6.

$$x=1$$

The system is now solved.

$$x=1 y=2 z=3$$