Leysa {l}{285a+45b+9c=74}{2025a+285b+452=421}{15333a+2025b+2856=2770}

$$\left. \begin{array} { l } { 285 a + 45 b + 9 c = 74 } \\ { 2025 a + 285 b + 452 = 421 } \\ { 15333 a + 2025 b + 2856 = 2770 } \end{array} \right.$$

Leystu fyrir a, b, c

$$a=\frac{2551}{17952}\approx 0.142101159$$

$$b = -\frac{100391}{89760} = -1\frac{10631}{89760} \approx -1.118438057$$

$$c = \frac{11401}{1224} = 9\frac{385}{1224} \approx 9.314542484$$

Styttri leiðir við notkun innsetningar

Leystu 285a+45b+9c=74 fyrir a.

$$a=-\frac{3}{19}b-\frac{3}{95}c+\frac{74}{285}$$

Settu -\frac{3}{19}b-\frac{3}{95}c+\frac{74}{285} inn fyrir a í annarri og þriðju jöfnu.

$$2025\left(-\frac{3}{19}b-\frac{3}{95}c+\frac{74}{285}\right)+285b+452=421 15333\left(-\frac{3}{19}b-\frac{3}{95}c+\frac{74}{285}\right)+2025b+2856=2770$$

Leystu þessar jöfnur fyrir b og c í þessari röð.

$$b=\frac{10579}{660}-\frac{81}{44}c c=\frac{20336}{2421}-\frac{220}{269}b$$

Settu \frac{10579}{660}-\frac{81}{44}c inn fyrir b í hinni jöfnunni c=\frac{20336}{2421}-\frac{220}{269}b.

$$c=\frac{20336}{2421}-\frac{220}{269}\left(\frac{10579}{660}-\frac{81}{44}c\right)$$

Leystu c=\frac{20336}{2421}-\frac{220}{269}\left(\frac{10579}{660}-\frac{81}{44}c\right) fyrir c.

$$c=\frac{11401}{1224}$$

Settu \frac{11401}{1224} inn fyrir c í hinni jöfnunni b=\frac{10579}{660}-\frac{81}{44}c.

$$b=\frac{10579}{660}-\frac{81}{44}\times \frac{11401}{1224}$$

Reiknaðu b frá b=\frac{10579}{660}-\frac{81}{44}\times \frac{11401}{1224}.

$$b=-\frac{100391}{89760}$$

Settu -\frac{100391}{89760} inn fyrir b og \frac{11401}{1224} fyrir c í jöfnunni a=-\frac{3}{19}b-\frac{3}{95}c+\frac{74}{285}.

$$a=-\frac{3}{19}\left(-\frac{100391}{89760}\right)-\frac{3}{95}\times \frac{11401}{1224}+\frac{74}{285}$$

Reiknaðu a frá a=-\frac{3}{19}\left(-\frac{100391}{89760}\right)-\frac{3}{95}\times \frac{11401}{1224}+\frac{74}{285}.

$$a=\frac{2551}{17952}$$

Leyst var úr kerfinu.

$$a=\frac{2551}{17952} b=-\frac{100391}{89760} c=\frac{11401}{1224}$$