Solve {l}{x+y+z=10}{x+y-z=5}{x-y+z=6}

$$\left. \begin{array} { l } { x + y + z = 10 } \\ { x + y - z = 5 } \\ { x - y + z = 6 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

$$y=2$$

$$z = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Short Steps Using Substitution

Solve x+y+z=10 for x.

$$x=-y-z+10$$

Substitute -y-z+10 for x in the second and third equation.

$$-y-z+10+y-z=5 -y-z+10-y+z=6$$

Solve these equations for z and y respectively.

$$z=\frac{5}{2} y=2$$

Substitute \frac{5}{2} for z and 2 for y in the equation x=-y-z+10.

$$x=-2-\frac{5}{2}+10$$

Calculate x from x=-2-\frac{5}{2}+10.

$$x=\frac{11}{2}$$

The system is now solved.

$$x=\frac{11}{2} y=2 z=\frac{5}{2}$$