Solve {r}{x+2y-z=-7}{x+z=3}{2x-y-z=-9}

$$\left\{ \begin{array} { r } { x + 2 y - z = - 7 } \\ { x + z = 3 } \\ { 2 x - y - z = - 9 } \end{array} \right.$$

Solve for x, y, z

$$x=-2$$

$$y=0$$

$$z=5$$

Short Steps Using Substitution

Solve x+2y-z=-7 for x.

$$x=-2y+z-7$$

Substitute -2y+z-7 for x in the second and third equation.

$$-2y+z-7+z=3 2\left(-2y+z-7\right)-y-z=-9$$

Solve these equations for y and z respectively.

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

Substitute -5+z for y in the equation z=5+5y.

$$z=5+5\left(-5+z\right)$$

Solve z=5+5\left(-5+z\right) for z.

$$z=5$$

Substitute 5 for z in the equation y=-5+z.

$$y=-5+5$$

Calculate y from y=-5+5.

$$y=0$$

Substitute 0 for y and 5 for z in the equation x=-2y+z-7.

$$x=-2\times 0+5-7$$

Calculate x from x=-2\times 0+5-7.

$$x=-2$$

The system is now solved.

$$x=-2 y=0 z=5$$