Solve {l}{x+y+z=10}{x+y-z=6}{x-y+z=3}

$$\left. \begin{array} { l } { x + y + z = 10 } \\ { x + y - z = 6 } \\ { x - y + z = 3 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

$$y = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

$$z=2$$

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.

$$-y-z+10+y-z=6 -y-z+10-y+z=3$$

Solve these equations for z and y respectively.

$$z=2 y=\frac{7}{2}$$

Substitute 2 for z and \frac{7}{2} for y in the equation x=-y-z+10.

$$x=-\frac{7}{2}-2+10$$

Calculate x from x=-\frac{7}{2}-2+10.

$$x=\frac{9}{2}$$

The system is now solved.

$$x=\frac{9}{2} y=\frac{7}{2} z=2$$