Solve {r}{-9x+4y-6z=16}{17x-14y-2z=-16}{x-16y-2z=-56}

$$\left. \begin{array} { r } { - 9 x + 4 y - 6 z = 16 } \\ { 17 x - 14 y - 2 z = - 16 } \\ { x - 16 y - 2 z = - 56 } \end{array} \right.$$

Solve for x, y, z

$$x=2$$

$$y=4$$

$$z=-3$$

Short Steps Using Substitution

Reorder the equations.

$$x-16y-2z=-56 17x-14y-2z=-16 -9x+4y-6z=16$$

Solve x-16y-2z=-56 for x.

$$x=-56+16y+2z$$

Substitute -56+16y+2z for x in the second and third equation.

$$17\left(-56+16y+2z\right)-14y-2z=-16 -9\left(-56+16y+2z\right)+4y-6z=16$$

Solve these equations for y and z respectively.

$$y=\frac{156}{43}-\frac{16}{129}z z=\frac{61}{3}-\frac{35}{6}y$$

Substitute \frac{156}{43}-\frac{16}{129}z for y in the equation z=\frac{61}{3}-\frac{35}{6}y.

$$z=\frac{61}{3}-\frac{35}{6}\left(\frac{156}{43}-\frac{16}{129}z\right)$$

Solve z=\frac{61}{3}-\frac{35}{6}\left(\frac{156}{43}-\frac{16}{129}z\right) for z.

$$z=-3$$

Substitute -3 for z in the equation y=\frac{156}{43}-\frac{16}{129}z.

$$y=\frac{156}{43}-\frac{16}{129}\left(-3\right)$$

Calculate y from y=\frac{156}{43}-\frac{16}{129}\left(-3\right).

$$y=4$$

Substitute 4 for y and -3 for z in the equation x=-56+16y+2z.

$$x=-56+16\times 4+2\left(-3\right)$$

Calculate x from x=-56+16\times 4+2\left(-3\right).

$$x=2$$

The system is now solved.

$$x=2 y=4 z=-3$$