Solve {l}{1954x-682y=5280}{330x-790y+220z=0}{210y-850z=-3360}

$$\left. \begin{array} { l } { 1954 x - 682 y = 5280 } \\ { 330 x - 790 y + 220 z = 0 } \\ { 210 y - 850 z = - 3360 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{4757148}{1288169} = 3\frac{892641}{1288169} \approx 3.692953331$$

$$y = \frac{3656796}{1288169} = 2\frac{1080458}{1288169} \approx 2.838754853$$

$$z = \frac{5995500}{1288169} = 4\frac{842824}{1288169} \approx 4.654280611$$

Short Steps Using Substitution

Solve 1954x-682y=5280 for x.

$$x=\frac{2640}{977}+\frac{341}{977}y$$

Substitute \frac{2640}{977}+\frac{341}{977}y for x in the equation 330x-790y+220z=0.

$$330\left(\frac{2640}{977}+\frac{341}{977}y\right)-790y+220z=0$$

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

$$y=\frac{8712}{6593}+\frac{10747}{32965}z z=\frac{336}{85}+\frac{21}{85}y$$

Substitute \frac{8712}{6593}+\frac{10747}{32965}z for y in the equation z=\frac{336}{85}+\frac{21}{85}y.

$$z=\frac{336}{85}+\frac{21}{85}\left(\frac{8712}{6593}+\frac{10747}{32965}z\right)$$

Solve z=\frac{336}{85}+\frac{21}{85}\left(\frac{8712}{6593}+\frac{10747}{32965}z\right) for z.

$$z=\frac{5995500}{1288169}$$

Substitute \frac{5995500}{1288169} for z in the equation y=\frac{8712}{6593}+\frac{10747}{32965}z.

$$y=\frac{8712}{6593}+\frac{10747}{32965}\times \frac{5995500}{1288169}$$

Calculate y from y=\frac{8712}{6593}+\frac{10747}{32965}\times \frac{5995500}{1288169}.

$$y=\frac{3656796}{1288169}$$

Substitute \frac{3656796}{1288169} for y in the equation x=\frac{2640}{977}+\frac{341}{977}y.

$$x=\frac{2640}{977}+\frac{341}{977}\times \frac{3656796}{1288169}$$

Calculate x from x=\frac{2640}{977}+\frac{341}{977}\times \frac{3656796}{1288169}.

$$x=\frac{4757148}{1288169}$$

The system is now solved.

$$x=\frac{4757148}{1288169} y=\frac{3656796}{1288169} z=\frac{5995500}{1288169}$$