Leysa {c}{-0.6834x-0.7544y-0.844z+200=0}{0.2563x+0.1961y-0.4472z=0}{0.6834z-0.5883y=0}

$$\left. \begin{array} { c } { - 0.6834 x - 0.7544 y - 0.844 z + 200 = 0 } \\ { 0.2563 x + 0.1961 y - 0.4472 z = 0 } \\ { 0.6834 z - 0.5883 y = 0 } \end{array} \right.$$

Leystu fyrir x, y, z

$$x = \frac{2151217000000}{28967096623} = 74\frac{7651849898}{28967096623} \approx 74.264156605$$

$$y = \frac{2919257000000}{28967096623} = 100\frac{22547337700}{28967096623} \approx 100.77837755$$

$$z = \frac{2513021500000}{28967096623} = 86\frac{21851190422}{28967096623} \approx 86.754345204$$

Styttri leiðir við notkun innsetningar

Leystu -0.6834x-0.7544y-0.844z+200=0 fyrir x.

$$x=-\frac{3772}{3417}y-\frac{4220}{3417}z+\frac{1000000}{3417}$$

Settu -\frac{3772}{3417}y-\frac{4220}{3417}z+\frac{1000000}{3417} inn fyrir x í hinni jöfnunni 0.2563x+0.1961y-0.4472z=0.

$$0.2563\left(-\frac{3772}{3417}y-\frac{4220}{3417}z+\frac{1000000}{3417}\right)+0.1961y-0.4472z=0$$

Leysa aðra jöfnu fyrir y og þá þriðju fyrir z.

$$y=\frac{2563000000}{2966899}-\frac{26096684}{2966899}z z=\frac{1961}{2278}y$$

Settu \frac{2563000000}{2966899}-\frac{26096684}{2966899}z inn fyrir y í hinni jöfnunni z=\frac{1961}{2278}y.

$$z=\frac{1961}{2278}\left(\frac{2563000000}{2966899}-\frac{26096684}{2966899}z\right)$$

Leystu z=\frac{1961}{2278}\left(\frac{2563000000}{2966899}-\frac{26096684}{2966899}z\right) fyrir z.

$$z=\frac{2513021500000}{28967096623}$$

Settu \frac{2513021500000}{28967096623} inn fyrir z í hinni jöfnunni y=\frac{2563000000}{2966899}-\frac{26096684}{2966899}z.

$$y=\frac{2563000000}{2966899}-\frac{26096684}{2966899}\times \frac{2513021500000}{28967096623}$$

Reiknaðu y frá y=\frac{2563000000}{2966899}-\frac{26096684}{2966899}\times \frac{2513021500000}{28967096623}.

$$y=\frac{2919257000000}{28967096623}$$

Settu \frac{2919257000000}{28967096623} inn fyrir y og \frac{2513021500000}{28967096623} fyrir z í jöfnunni x=-\frac{3772}{3417}y-\frac{4220}{3417}z+\frac{1000000}{3417}.

$$x=-\frac{3772}{3417}\times \frac{2919257000000}{28967096623}-\frac{4220}{3417}\times \frac{2513021500000}{28967096623}+\frac{1000000}{3417}$$

Reiknaðu x frá x=-\frac{3772}{3417}\times \frac{2919257000000}{28967096623}-\frac{4220}{3417}\times \frac{2513021500000}{28967096623}+\frac{1000000}{3417}.

$$x=\frac{2151217000000}{28967096623}$$

Leyst var úr kerfinu.

$$x=\frac{2151217000000}{28967096623} y=\frac{2919257000000}{28967096623} z=\frac{2513021500000}{28967096623}$$