Solve {l}{x+y+z=6}{y+3z=11}{x-2y+z=0}

$$\left. \begin{array} { l } { x + y + z = 6 } \\ { y + 3 z = 11 } \\ { x - 2 y + z = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=1$$

$$y=2$$

$$z=3$$

Short Steps Using Substitution

Solve x+y+z=6 for x.

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

Substitute -y-z+6 for x in the equation x-2y+z=0.

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

Solve the second equation for z and the third equation for y.

$$z=-\frac{1}{3}y+\frac{11}{3} y=2$$

Substitute 2 for y in the equation z=-\frac{1}{3}y+\frac{11}{3}.

$$z=-\frac{1}{3}\times 2+\frac{11}{3}$$

Calculate z from z=-\frac{1}{3}\times 2+\frac{11}{3}.

$$z=3$$

Substitute 3 for z and 2 for y 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.

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