Solve {c}{x+y-z=1-6}{3x+y-2z=3-2}{x-y-z=-1-3}

$$\left. \begin{array} { c } { x + y - z = 1 - 6 } \\ { 3 x + y - 2 z = 3 - 2 } \\ { x - y - z = - 1 - 3 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{21}{2} = 10\frac{1}{2} = 10.5$$

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

$$z=15$$

Short Steps Using Substitution

Solve x+y-z=1-6 for x.

$$x=-y+z-5$$

Substitute -y+z-5 for x in the second and third equation.

$$3\left(-y+z-5\right)+y-2z=3-2 -y+z-5-y-z=-1-3$$

Solve these equations for z and y respectively.

$$z=16+2y y=-\frac{1}{2}$$

Substitute -\frac{1}{2} for y in the equation z=16+2y.

$$z=16+2\left(-\frac{1}{2}\right)$$

Calculate z from z=16+2\left(-\frac{1}{2}\right).

$$z=15$$

Substitute 15 for z and -\frac{1}{2} for y in the equation x=-y+z-5.

$$x=-\left(-\frac{1}{2}\right)+15-5$$

Calculate x from x=-\left(-\frac{1}{2}\right)+15-5.

$$x=\frac{21}{2}$$

The system is now solved.

$$x=\frac{21}{2} y=-\frac{1}{2} z=15$$