Solve {c}{2x-y-z=6}{3x-2y+3z=-13}{y+3z=-16}

$$\left. \begin{array} { c } { 2 x - y - z = 6 } \\ { 3 x - 2 y + 3 z = - 13 } \\ { y + 3 z = - 16 } \end{array} \right.$$

Solve for x, y, z

$$x=0$$

$$y=-1$$

$$z=-5$$

Short Steps Using Substitution

Solve 2x-y-z=6 for y.

$$y=2x-z-6$$

Substitute 2x-z-6 for y in the second and third equation.

$$3x-2\left(2x-z-6\right)+3z=-13 2x-z-6+3z=-16$$

Solve these equations for x and z respectively.

$$x=25+5z z=-5-x$$

Substitute 25+5z for x in the equation z=-5-x.

$$z=-5-\left(25+5z\right)$$

Solve z=-5-\left(25+5z\right) for z.

$$z=-5$$

Substitute -5 for z in the equation x=25+5z.

$$x=25+5\left(-5\right)$$

Calculate x from x=25+5\left(-5\right).

$$x=0$$

Substitute 0 for x and -5 for z in the equation y=2x-z-6.

$$y=2\times 0-\left(-5\right)-6$$

Calculate y from y=2\times 0-\left(-5\right)-6.

$$y=-1$$

The system is now solved.

$$x=0 y=-1 z=-5$$