Solve {c}{-4x-7y+z=-18}{-5x+2y+10z=-38}{2x+9y-4z=25}

$$\left. \begin{array} { c } { - 4 x - 7 y + z = - 18 } \\ { - 5 x + 2 y + 10 z = - 38 } \\ { 2 x + 9 y - 4 z = 25 } \end{array} \right.$$

Solve for x, y, z

$$x=2$$

$$y=1$$

$$z=-3$$

Short Steps Using Substitution

Solve -4x-7y+z=-18 for z.

$$z=4x+7y-18$$

Substitute 4x+7y-18 for z in the second and third equation.

$$-5x+2y+10\left(4x+7y-18\right)=-38 2x+9y-4\left(4x+7y-18\right)=25$$

Solve these equations for y and x respectively.

$$y=-\frac{35}{72}x+\frac{71}{36} x=-\frac{19}{14}y+\frac{47}{14}$$

Substitute -\frac{35}{72}x+\frac{71}{36} for y in the equation x=-\frac{19}{14}y+\frac{47}{14}.

$$x=-\frac{19}{14}\left(-\frac{35}{72}x+\frac{71}{36}\right)+\frac{47}{14}$$

Solve x=-\frac{19}{14}\left(-\frac{35}{72}x+\frac{71}{36}\right)+\frac{47}{14} for x.

$$x=2$$

Substitute 2 for x in the equation y=-\frac{35}{72}x+\frac{71}{36}.

$$y=-\frac{35}{72}\times 2+\frac{71}{36}$$

Calculate y from y=-\frac{35}{72}\times 2+\frac{71}{36}.

$$y=1$$

Substitute 1 for y and 2 for x in the equation z=4x+7y-18.

$$z=4\times 2+7\times 1-18$$

Calculate z from z=4\times 2+7\times 1-18.

$$z=-3$$

The system is now solved.

$$x=2 y=1 z=-3$$