सोडोवचें {l}{x_{1}-x_{2}+x_{3}=2}{x_{1}+2x_{2}=1}{x_{1}-x_{3}=4}

$$\left\{ \begin{array}{l}{ x _ { 1 } - x _ { 2 } + x _ { 3 } = 2 }\\{ x _ { 1 } + 2 x _ { 2 } = 1 }\\{ x _ { 1 } - x _ { 3 } = 4 }\end{array} \right.$$

x_1, x_2, x_3 खातीर सोडोवचें

$$x_{1} = \frac{13}{5} = 2\frac{3}{5} = 2.6$$

$$x_{2}=-\frac{4}{5}=-0.8$$

$$x_{3} = -\frac{7}{5} = -1\frac{2}{5} = -1.4$$

बदली वापरून संक्षिप्त पांवडे

x_{1} खातीर x_{1}-x_{2}+x_{3}=2 सोडोवचो.

$$x_{1}=x_{2}-x_{3}+2$$

दुस-या आनी तिस-या समिकरणांत x_{1} खातीर x_{2}-x_{3}+2 बदलपी घेवचो.

$$x_{2}-x_{3}+2+2x_{2}=1 x_{2}-x_{3}+2-x_{3}=4$$

अनुक्रमान x_{2} आनी x_{3} खातीर हीं समिकरणां सोडोवचीं.

$$x_{2}=-\frac{1}{3}+\frac{1}{3}x_{3} x_{3}=-1+\frac{1}{2}x_{2}$$

x_{3}=-1+\frac{1}{2}x_{2} ह्या समिकरणांत x_{2} खातीर -\frac{1}{3}+\frac{1}{3}x_{3} बदलपी घेवचो.

$$x_{3}=-1+\frac{1}{2}\left(-\frac{1}{3}+\frac{1}{3}x_{3}\right)$$

x_{3} खातीर x_{3}=-1+\frac{1}{2}\left(-\frac{1}{3}+\frac{1}{3}x_{3}\right) सोडोवचो.

$$x_{3}=-\frac{7}{5}$$

x_{2}=-\frac{1}{3}+\frac{1}{3}x_{3} ह्या समिकरणांत x_{3} खातीर -\frac{7}{5} बदलपी घेवचो.

$$x_{2}=-\frac{1}{3}+\frac{1}{3}\left(-\frac{7}{5}\right)$$

x_{2}=-\frac{1}{3}+\frac{1}{3}\left(-\frac{7}{5}\right) तल्यान x_{2} मेजचो.

$$x_{2}=-\frac{4}{5}$$

x_{2} आनी -\frac{7}{5} ह्या समिकरणांत x_{3} खातीर -\frac{4}{5} बदलपी घेवचो x_{1}=x_{2}-x_{3}+2.

$$x_{1}=-\frac{4}{5}-\left(-\frac{7}{5}\right)+2$$

x_{1}=-\frac{4}{5}-\left(-\frac{7}{5}\right)+2 तल्यान x_{1} मेजचो.

$$x_{1}=\frac{13}{5}$$

प्रणाली आतां सुटावी जाली.

$$x_{1}=\frac{13}{5} x_{2}=-\frac{4}{5} x_{3}=-\frac{7}{5}$$