Solve {l}{5x-4y=1}{-4x+11y-5z=2}{-5y+8z=-3}

$$\left. \begin{array}{l}{ 5 x - 4 y = 1 }\\{ - 4 x + 11 y - 5 z = 2 }\\{ - 5 y + 8 z = - 3 }\end{array} \right.$$

Solve for x, y, z

$$x=\frac{67}{187}\approx 0.35828877$$

$$y=\frac{37}{187}\approx 0.197860963$$

$$z=-\frac{47}{187}\approx -0.251336898$$

Short Steps Using Substitution

Solve 5x-4y=1 for x.

$$x=\frac{4}{5}y+\frac{1}{5}$$

Substitute \frac{4}{5}y+\frac{1}{5} for x in the equation -4x+11y-5z=2.

$$-4\left(\frac{4}{5}y+\frac{1}{5}\right)+11y-5z=2$$

Solve the second equation for y and the third equation for z.

$$y=\frac{14}{39}+\frac{25}{39}z z=\frac{5}{8}y-\frac{3}{8}$$

Substitute \frac{14}{39}+\frac{25}{39}z for y in the equation z=\frac{5}{8}y-\frac{3}{8}.

$$z=\frac{5}{8}\left(\frac{14}{39}+\frac{25}{39}z\right)-\frac{3}{8}$$

Solve z=\frac{5}{8}\left(\frac{14}{39}+\frac{25}{39}z\right)-\frac{3}{8} for z.

$$z=-\frac{47}{187}$$

Substitute -\frac{47}{187} for z in the equation y=\frac{14}{39}+\frac{25}{39}z.

$$y=\frac{14}{39}+\frac{25}{39}\left(-\frac{47}{187}\right)$$

Calculate y from y=\frac{14}{39}+\frac{25}{39}\left(-\frac{47}{187}\right).

$$y=\frac{37}{187}$$

Substitute \frac{37}{187} for y in the equation x=\frac{4}{5}y+\frac{1}{5}.

$$x=\frac{4}{5}\times \frac{37}{187}+\frac{1}{5}$$

Calculate x from x=\frac{4}{5}\times \frac{37}{187}+\frac{1}{5}.

$$x=\frac{67}{187}$$

The system is now solved.

$$x=\frac{67}{187} y=\frac{37}{187} z=-\frac{47}{187}$$