सोडोवचें {l}{x_{1}+x_{2}-3x_{3}-2x_{4}=2}{x_{1}+x_{3}-x_{4}=1}{2x_{1}+6x_{2}-13x_{3}-5x_{4}=6}

$$\left. \begin{array}{l}{ x _ { 1 } + x _ { 2 } - 3 x _ { 3 } - 2 x _ { 4 } = 2 }\\{ x _ { 1 } + x _ { 3 } - x _ { 4 } = 1 }\\{ 2 x _ { 1 } + 6 x _ { 2 } - 13 x _ { 3 } - 5 x _ { 4 } = 6 }\end{array} \right.$$

x_1, x_2, x_3 खातीर सोडोवचें

$$x_{1}=\frac{4x_{4}}{3}+\frac{11}{9}$$

$$x_{2}=-\frac{x_{4}}{3}+\frac{1}{9}$$

$$x_{3}=-\frac{x_{4}}{3}-\frac{2}{9}$$

बदली वापरून संक्षिप्त पांवडे

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

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

दुस-या आनी तिस-या समिकरणांत x_{1} खातीर -x_{2}+3x_{3}+2x_{4}+2 बदलपी घेवचो.

$$-x_{2}+3x_{3}+2x_{4}+2+x_{3}-x_{4}=1 2\left(-x_{2}+3x_{3}+2x_{4}+2\right)+6x_{2}-13x_{3}-5x_{4}=6$$

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

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

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

$$x_{3}=\frac{4}{7}\left(4x_{3}+x_{4}+1\right)-\frac{1}{7}x_{4}-\frac{2}{7}$$

x_{3} खातीर x_{3}=\frac{4}{7}\left(4x_{3}+x_{4}+1\right)-\frac{1}{7}x_{4}-\frac{2}{7} सोडोवचो.

$$x_{3}=-\frac{2}{9}-\frac{1}{3}x_{4}$$

x_{2}=4x_{3}+x_{4}+1 ह्या समिकरणांत x_{3} खातीर -\frac{2}{9}-\frac{1}{3}x_{4} बदलपी घेवचो.

$$x_{2}=4\left(-\frac{2}{9}-\frac{1}{3}x_{4}\right)+x_{4}+1$$

x_{2}=4\left(-\frac{2}{9}-\frac{1}{3}x_{4}\right)+x_{4}+1 तल्यान x_{2} मेजचो.

$$x_{2}=\frac{1}{9}-\frac{1}{3}x_{4}$$

x_{2} आनी -\frac{2}{9}-\frac{1}{3}x_{4} ह्या समिकरणांत x_{3} खातीर \frac{1}{9}-\frac{1}{3}x_{4} बदलपी घेवचो x_{1}=-x_{2}+3x_{3}+2x_{4}+2.

$$x_{1}=-\left(\frac{1}{9}-\frac{1}{3}x_{4}\right)+3\left(-\frac{2}{9}-\frac{1}{3}x_{4}\right)+2x_{4}+2$$

x_{1}=-\left(\frac{1}{9}-\frac{1}{3}x_{4}\right)+3\left(-\frac{2}{9}-\frac{1}{3}x_{4}\right)+2x_{4}+2 तल्यान x_{1} मेजचो.

$$x_{1}=\frac{11}{9}+\frac{4}{3}x_{4}$$

प्रणाली आतां सुटावी जाली.

$$x_{1}=\frac{11}{9}+\frac{4}{3}x_{4} x_{2}=\frac{1}{9}-\frac{1}{3}x_{4} x_{3}=-\frac{2}{9}-\frac{1}{3}x_{4}$$