Solve {r}{4x+3y-2z=-11}{-3x-7y+3z=10}{-9x-8y+5z=9}

$$\left. \begin{array} { r } { 4 x + 3 y - 2 z = - 11 } \\ { - 3 x - 7 y + 3 z = 10 } \\ { - 9 x - 8 y + 5 z = 9 } \end{array} \right.$$

Solve for x, y, z

$$x=-43$$

$$y=-49$$

$$z=-154$$

Short Steps Using Substitution

Solve 4x+3y-2z=-11 for x.

$$x=-\frac{3}{4}y+\frac{1}{2}z-\frac{11}{4}$$

Substitute -\frac{3}{4}y+\frac{1}{2}z-\frac{11}{4} for x in the second and third equation.

$$-3\left(-\frac{3}{4}y+\frac{1}{2}z-\frac{11}{4}\right)-7y+3z=10 -9\left(-\frac{3}{4}y+\frac{1}{2}z-\frac{11}{4}\right)-8y+5z=9$$

Solve these equations for y and z respectively.

$$y=-\frac{7}{19}+\frac{6}{19}z z=-\frac{63}{2}+\frac{5}{2}y$$

Substitute -\frac{7}{19}+\frac{6}{19}z for y in the equation z=-\frac{63}{2}+\frac{5}{2}y.

$$z=-\frac{63}{2}+\frac{5}{2}\left(-\frac{7}{19}+\frac{6}{19}z\right)$$

Solve z=-\frac{63}{2}+\frac{5}{2}\left(-\frac{7}{19}+\frac{6}{19}z\right) for z.

$$z=-154$$

Substitute -154 for z in the equation y=-\frac{7}{19}+\frac{6}{19}z.

$$y=-\frac{7}{19}+\frac{6}{19}\left(-154\right)$$

Calculate y from y=-\frac{7}{19}+\frac{6}{19}\left(-154\right).

$$y=-49$$

Substitute -49 for y and -154 for z in the equation x=-\frac{3}{4}y+\frac{1}{2}z-\frac{11}{4}.

$$x=-\frac{3}{4}\left(-49\right)+\frac{1}{2}\left(-154\right)-\frac{11}{4}$$

Calculate x from x=-\frac{3}{4}\left(-49\right)+\frac{1}{2}\left(-154\right)-\frac{11}{4}.

$$x=-43$$

The system is now solved.

$$x=-43 y=-49 z=-154$$