Solve {l}{x+y+z=3}{x-y+z=1}{x+y-z=4}

$$\left. \begin{array} { l } { x + y + z = 3 } \\ { x - y + z = 1 } \\ { x + y - z = 4 } \end{array} \right.$$

Solve for x, y, z

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

$$y=1$$

$$z=-\frac{1}{2}=-0.5$$

Short Steps Using Substitution

Solve x+y+z=3 for x.

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

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

$$-y-z+3-y+z=1 -y-z+3+y-z=4$$

Solve these equations for y and z respectively.

$$y=1 z=-\frac{1}{2}$$

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

$$x=-1-\left(-\frac{1}{2}\right)+3$$

Calculate x from x=-1-\left(-\frac{1}{2}\right)+3.

$$x=\frac{5}{2}$$

The system is now solved.

$$x=\frac{5}{2} y=1 z=-\frac{1}{2}$$