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

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

I-solve ang x, y, z

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

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

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

Maiikling Hakbang sa Paggamit ng Substitution

Lutasin ang -0.6834x-0.7544y-0.844z+200=0 para sa x.

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

I-substitute ang -\frac{3772}{3417}y-\frac{4220}{3417}z+\frac{1000000}{3417} para sa x sa equation na 0.2563x+0.1961y-0.4472z=0.

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

Lutasin ang pangalawang equation para sa y at ang pangatlong equation para sa z.

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

I-substitute ang \frac{2563000000}{2966899}-\frac{26096684}{2966899}z para sa y sa equation na z=\frac{1961}{2278}y.

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

Lutasin ang z=\frac{1961}{2278}\left(\frac{2563000000}{2966899}-\frac{26096684}{2966899}z\right) para sa z.

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

I-substitute ang \frac{2513021500000}{28967096623} para sa z sa equation na y=\frac{2563000000}{2966899}-\frac{26096684}{2966899}z.

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

Kalkulahin ang y mula sa y=\frac{2563000000}{2966899}-\frac{26096684}{2966899}\times \frac{2513021500000}{28967096623}.

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

I-substitute ang \frac{2919257000000}{28967096623} para sa y at ang \frac{2513021500000}{28967096623} para sa z sa equation na x=-\frac{3772}{3417}y-\frac{4220}{3417}z+\frac{1000000}{3417}.

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

Kalkulahin ang x mula sa x=-\frac{3772}{3417}\times \frac{2919257000000}{28967096623}-\frac{4220}{3417}\times \frac{2513021500000}{28967096623}+\frac{1000000}{3417}.

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

Nalutas na ang system.

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