सोडोवचें {l}{1+3r+2s=13-2t}{5r-s=-21+3t}{2+8r+14s=14-t}

$$\left\{ \begin{array} { l } { 1 + 3 r + 2 s = 13 - 2 t } \\ { 5 r - s = - 21 + 3 t } \\ { 2 + 8 r + 14 s = 14 - t } \end{array} \right.$$

r, s, t खातीर सोडोवचें

$$r=-\frac{6}{13}\approx -0.461538462$$

$$t=6$$

$$s=\frac{9}{13}\approx 0.692307692$$

बदली वापरून संक्षिप्त पांवडे

समिकरणांचो क्रम परत लावचो.

$$5r-s=-21+3t 1+3r+2s=13-2t 2+8r+14s=14-t$$

s खातीर 5r-s=-21+3t सोडोवचो.

$$s=5r+21-3t$$

दुस-या आनी तिस-या समिकरणांत s खातीर 5r+21-3t बदलपी घेवचो.

$$1+3r+2\left(5r+21-3t\right)=13-2t 2+8r+14\left(5r+21-3t\right)=14-t$$

अनुक्रमान r आनी t खातीर हीं समिकरणां सोडोवचीं.

$$r=-\frac{30}{13}+\frac{4}{13}t t=\frac{282}{41}+\frac{78}{41}r$$

t=\frac{282}{41}+\frac{78}{41}r ह्या समिकरणांत r खातीर -\frac{30}{13}+\frac{4}{13}t बदलपी घेवचो.

$$t=\frac{282}{41}+\frac{78}{41}\left(-\frac{30}{13}+\frac{4}{13}t\right)$$

t खातीर t=\frac{282}{41}+\frac{78}{41}\left(-\frac{30}{13}+\frac{4}{13}t\right) सोडोवचो.

$$t=6$$

r=-\frac{30}{13}+\frac{4}{13}t ह्या समिकरणांत t खातीर 6 बदलपी घेवचो.

$$r=-\frac{30}{13}+\frac{4}{13}\times 6$$

r=-\frac{30}{13}+\frac{4}{13}\times 6 तल्यान r मेजचो.

$$r=-\frac{6}{13}$$

r आनी 6 ह्या समिकरणांत t खातीर -\frac{6}{13} बदलपी घेवचो s=5r+21-3t.

$$s=5\left(-\frac{6}{13}\right)+21-3\times 6$$

s=5\left(-\frac{6}{13}\right)+21-3\times 6 तल्यान s मेजचो.

$$s=\frac{9}{13}$$

प्रणाली आतां सुटावी जाली.

$$r=-\frac{6}{13} s=\frac{9}{13} t=6$$