Solve {l}{-4x+3y+z=7}{2+5x+y=3z}{2x-2z-4=-5}

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

Solve for x, y, z

$$x=-\frac{8}{9}\approx -0.888888889$$

$$y = \frac{23}{18} = 1\frac{5}{18} \approx 1.277777778$$

$$z=-\frac{7}{18}\approx -0.388888889$$

Short Steps Using Substitution

Solve -4x+3y+z=7 for z.

$$z=4x-3y+7$$

Substitute 4x-3y+7 for z in the second and third equation.

$$2+5x+y=3\left(4x-3y+7\right) 2x-2\left(4x-3y+7\right)-4=-5$$

Solve these equations for y and x respectively.

$$y=\frac{19}{10}+\frac{7}{10}x x=y-\frac{13}{6}$$

Substitute \frac{19}{10}+\frac{7}{10}x for y in the equation x=y-\frac{13}{6}.

$$x=\frac{19}{10}+\frac{7}{10}x-\frac{13}{6}$$

Solve x=\frac{19}{10}+\frac{7}{10}x-\frac{13}{6} for x.

$$x=-\frac{8}{9}$$

Substitute -\frac{8}{9} for x in the equation y=\frac{19}{10}+\frac{7}{10}x.

$$y=\frac{19}{10}+\frac{7}{10}\left(-\frac{8}{9}\right)$$

Calculate y from y=\frac{19}{10}+\frac{7}{10}\left(-\frac{8}{9}\right).

$$y=\frac{23}{18}$$

Substitute \frac{23}{18} for y and -\frac{8}{9} for x in the equation z=4x-3y+7.

$$z=4\left(-\frac{8}{9}\right)-3\times \frac{23}{18}+7$$

Calculate z from z=4\left(-\frac{8}{9}\right)-3\times \frac{23}{18}+7.

$$z=-\frac{7}{18}$$

The system is now solved.

$$x=-\frac{8}{9} y=\frac{23}{18} z=-\frac{7}{18}$$