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

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

Solve for x, y, z

$$x=-1$$

$$y=-1$$

$$z=2$$

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.

$$y=-\frac{73}{37}+\frac{18}{37}z z=\frac{135}{38}+\frac{59}{38}y$$

Substitute -\frac{73}{37}+\frac{18}{37}z for y in the equation z=\frac{135}{38}+\frac{59}{38}y.

$$z=\frac{135}{38}+\frac{59}{38}\left(-\frac{73}{37}+\frac{18}{37}z\right)$$

Solve z=\frac{135}{38}+\frac{59}{38}\left(-\frac{73}{37}+\frac{18}{37}z\right) for z.

$$z=2$$

Substitute 2 for z in the equation y=-\frac{73}{37}+\frac{18}{37}z.

$$y=-\frac{73}{37}+\frac{18}{37}\times 2$$

Calculate y from y=-\frac{73}{37}+\frac{18}{37}\times 2.

$$y=-1$$

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

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

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

$$x=-1$$

The system is now solved.

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