Solve {l}{x+y+3z=14}{x+y+2z=11}{x+2y-z=5}

$$\left\{ \begin{array} { l } { x + y + 3 z = 14 } \\ { x + y + 2 z = 11 } \\ { x + 2 y - z = 5 } \end{array} \right.$$

Solve for x, y, z

$$x=2$$

$$y=3$$

$$z=3$$

Short Steps Using Substitution

Solve x+y+3z=14 for x.

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

Substitute -y-3z+14 for x in the second and third equation.

$$-y-3z+14+y+2z=11 -y-3z+14+2y-z=5$$

Solve these equations for z and y respectively.

$$z=3 y=4z-9$$

Substitute 3 for z in the equation y=4z-9.

$$y=4\times 3-9$$

Calculate y from y=4\times 3-9.

$$y=3$$

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

$$x=-3-3\times 3+14$$

Calculate x from x=-3-3\times 3+14.

$$x=2$$

The system is now solved.

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