Leysa {l}{36=I_{1}(9+4)-I_{2}(-9-4)-[3(0)}{0=I_{1}(-9-4)+I_{2}(4+9+6)-I_{3}(-6)}{0=I_{1}(0)-I_{2}(-6)+I_{3}(6+3+6)}

$$\left. \begin{array} { l } { 36 = I _ { 1 } ( 9 + 4 ) - I _ { 2 } ( - 9 - 4 ) - [ 3 ( 0 ) } \\ { 0 = I _ { 1 } ( - 9 - 4 ) + I _ { 2 } ( 4 + 9 + 6 ) - I _ { 3 } ( - 6 ) } \\ { 0 = I _ { 1 } ( 0 ) - I _ { 2 } ( - 6 ) + I _ { 3 } ( 6 + 3 + 6 ) } \end{array} \right.$$

Leystu fyrir I_1, I_2, I_3

$$I_{1} = \frac{747}{481} = 1\frac{266}{481} \approx 1.553014553$$

$$I_{2} = \frac{45}{37} = 1\frac{8}{37} \approx 1.216216216$$

$$I_{3}=-\frac{18}{37}\approx -0.486486486$$

Styttri leiðir við notkun innsetningar

Leystu 36=I_{1}\left(9+4\right)-I_{2}\left(-9-4\right)-3\times 0 fyrir I_{1}.

$$I_{1}=-I_{2}+\frac{36}{13}$$

Settu -I_{2}+\frac{36}{13} inn fyrir I_{1} í annarri og þriðju jöfnu.

$$0=\left(-I_{2}+\frac{36}{13}\right)\left(-9-4\right)+I_{2}\left(4+9+6\right)-I_{3}\left(-6\right) 0=\left(-I_{2}+\frac{36}{13}\right)\times 0-I_{2}\left(-6\right)+I_{3}\left(6+3+6\right)$$

Leystu þessar jöfnur fyrir I_{2} og I_{3} í þessari röð.

$$I_{2}=\frac{9}{8}-\frac{3}{16}I_{3} I_{3}=-\frac{2}{5}I_{2}$$

Settu \frac{9}{8}-\frac{3}{16}I_{3} inn fyrir I_{2} í hinni jöfnunni I_{3}=-\frac{2}{5}I_{2}.

$$I_{3}=-\frac{2}{5}\left(\frac{9}{8}-\frac{3}{16}I_{3}\right)$$

Leystu I_{3}=-\frac{2}{5}\left(\frac{9}{8}-\frac{3}{16}I_{3}\right) fyrir I_{3}.

$$I_{3}=-\frac{18}{37}$$

Settu -\frac{18}{37} inn fyrir I_{3} í hinni jöfnunni I_{2}=\frac{9}{8}-\frac{3}{16}I_{3}.

$$I_{2}=\frac{9}{8}-\frac{3}{16}\left(-\frac{18}{37}\right)$$

Reiknaðu I_{2} frá I_{2}=\frac{9}{8}-\frac{3}{16}\left(-\frac{18}{37}\right).

$$I_{2}=\frac{45}{37}$$

Settu \frac{45}{37} inn fyrir I_{2} í hinni jöfnunni I_{1}=-I_{2}+\frac{36}{13}.

$$I_{1}=-\frac{45}{37}+\frac{36}{13}$$

Reiknaðu I_{1} frá I_{1}=-\frac{45}{37}+\frac{36}{13}.

$$I_{1}=\frac{747}{481}$$

Leyst var úr kerfinu.

$$I_{1}=\frac{747}{481} I_{2}=\frac{45}{37} I_{3}=-\frac{18}{37}$$