सोडोवचें {l}{4x_{1}+2x_{2}-x_{3}=2}{3x_{1}-x_{2}+2x_{3}=10}{11x_{1}+x_{2}=8}

$$\left\{ \begin{array} { l } { 4 x _ { 1 } + 2 x _ { 2 } - x _ { 3 } = 2 } \\ { 3 x _ { 1 } - x _ { 2 } + 2 x _ { 3 } = 10 } \\ { 11 x _ { 1 } + x _ { 2 } = 8 } \end{array} \right.$$

x_1, x_2, x_3 खातीर सोडोवचें

$$x_{1}=\frac{5}{11}\approx 0.454545455$$

$$x_{2}=3$$

$$x_{3} = \frac{64}{11} = 5\frac{9}{11} \approx 5.818181818$$

बदली वापरून संक्षिप्त पांवडे

x_{3} खातीर 4x_{1}+2x_{2}-x_{3}=2 सोडोवचो.

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

3x_{1}-x_{2}+2x_{3}=10 ह्या समिकरणांत x_{3} खातीर -2+4x_{1}+2x_{2} बदलपी घेवचो.

$$3x_{1}-x_{2}+2\left(-2+4x_{1}+2x_{2}\right)=10$$

x_{2} खातीर दुसरें समिकरण आनी x_{1} खातीर तिसरें समिकरण सोडोवचें.

$$x_{2}=-\frac{11}{3}x_{1}+\frac{14}{3} x_{1}=-\frac{1}{11}x_{2}+\frac{8}{11}$$

x_{1}=-\frac{1}{11}x_{2}+\frac{8}{11} ह्या समिकरणांत x_{2} खातीर -\frac{11}{3}x_{1}+\frac{14}{3} बदलपी घेवचो.

$$x_{1}=-\frac{1}{11}\left(-\frac{11}{3}x_{1}+\frac{14}{3}\right)+\frac{8}{11}$$

x_{1} खातीर x_{1}=-\frac{1}{11}\left(-\frac{11}{3}x_{1}+\frac{14}{3}\right)+\frac{8}{11} सोडोवचो.

$$x_{1}=\frac{5}{11}$$

x_{2}=-\frac{11}{3}x_{1}+\frac{14}{3} ह्या समिकरणांत x_{1} खातीर \frac{5}{11} बदलपी घेवचो.

$$x_{2}=-\frac{11}{3}\times \frac{5}{11}+\frac{14}{3}$$

x_{2}=-\frac{11}{3}\times \frac{5}{11}+\frac{14}{3} तल्यान x_{2} मेजचो.

$$x_{2}=3$$

x_{2} आनी \frac{5}{11} ह्या समिकरणांत x_{1} खातीर 3 बदलपी घेवचो x_{3}=-2+4x_{1}+2x_{2}.

$$x_{3}=-2+4\times \frac{5}{11}+2\times 3$$

x_{3}=-2+4\times \frac{5}{11}+2\times 3 तल्यान x_{3} मेजचो.

$$x_{3}=\frac{64}{11}$$

प्रणाली आतां सुटावी जाली.

$$x_{1}=\frac{5}{11} x_{2}=3 x_{3}=\frac{64}{11}$$