Solve {l}{x=y+z}{6-2200x-1000z=0}{1000z-1200y+5=0}

$$\left\{ \begin{array} { l } { x = y + z } \\ { 6 - 2200 x - 1000 z = 0 } \\ { 1000 z - 1200 y + 5 = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{91}{30200}\approx 0.003013245$$

$$y=\frac{11}{3020}\approx 0.003642384$$

$$z=-\frac{19}{30200}\approx -0.000629139$$

Short Steps Using Substitution

Substitute y+z for x in the equation 6-2200x-1000z=0.

$$6-2200\left(y+z\right)-1000z=0$$

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

$$y=-\frac{16}{11}z+\frac{3}{1100} z=-\frac{1}{200}+\frac{6}{5}y$$

Substitute -\frac{16}{11}z+\frac{3}{1100} for y in the equation z=-\frac{1}{200}+\frac{6}{5}y.

$$z=-\frac{1}{200}+\frac{6}{5}\left(-\frac{16}{11}z+\frac{3}{1100}\right)$$

Solve z=-\frac{1}{200}+\frac{6}{5}\left(-\frac{16}{11}z+\frac{3}{1100}\right) for z.

$$z=-\frac{19}{30200}$$

Substitute -\frac{19}{30200} for z in the equation y=-\frac{16}{11}z+\frac{3}{1100}.

$$y=-\frac{16}{11}\left(-\frac{19}{30200}\right)+\frac{3}{1100}$$

Calculate y from y=-\frac{16}{11}\left(-\frac{19}{30200}\right)+\frac{3}{1100}.

$$y=\frac{11}{3020}$$

Substitute \frac{11}{3020} for y and -\frac{19}{30200} for z in the equation x=y+z.

$$x=\frac{11}{3020}-\frac{19}{30200}$$

Calculate x from x=\frac{11}{3020}-\frac{19}{30200}.

$$x=\frac{91}{30200}$$

The system is now solved.

$$x=\frac{91}{30200} y=\frac{11}{3020} z=-\frac{19}{30200}$$