Solve {l}{x+y+z=11}{x-y+3z=13}{2x+2y-z=7}

$$\left\{ \begin{array} { l } { x + y + z = 11 } \\ { x - y + 3 z = 13 } \\ { 2 x + 2 y - z = 7 } \end{array} \right.$$

Solve for x, y, z

$$x=2$$

$$y=4$$

$$z=5$$

Short Steps Using Substitution

Solve x+y+z=11 for x.

$$x=-y-z+11$$

Substitute -y-z+11 for x in the second and third equation.

$$-y-z+11-y+3z=13 2\left(-y-z+11\right)+2y-z=7$$

Solve these equations for y and z respectively.

$$y=-1+z z=5$$

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

$$y=-1+5$$

Calculate y from y=-1+5.

$$y=4$$

Substitute 4 for y and 5 for z in the equation x=-y-z+11.

$$x=-4-5+11$$

Calculate x from x=-4-5+11.

$$x=2$$

The system is now solved.

$$x=2 y=4 z=5$$