सोडोवचें {l}{x+y-z=2}{-x+2y+3z=-1}{x-4y-2z=-7}

$$\left. \begin{array} { l } { x + y - z = 2 } \\ { - x + 2 y + 3 z = - 1 } \\ { x - 4 y - 2 z = - 7 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x = -\frac{25}{7} = -3\frac{4}{7} \approx -3.571428571$$

$$y = \frac{17}{7} = 2\frac{3}{7} \approx 2.428571429$$

$$z = -\frac{22}{7} = -3\frac{1}{7} \approx -3.142857143$$

बदली वापरून संक्षिप्त पांवडे

x खातीर x+y-z=2 सोडोवचो.

$$x=-y+z+2$$

दुस-या आनी तिस-या समिकरणांत x खातीर -y+z+2 बदलपी घेवचो.

$$-\left(-y+z+2\right)+2y+3z=-1 -y+z+2-4y-2z=-7$$

अनुक्रमान y आनी z खातीर हीं समिकरणां सोडोवचीं.

$$y=-\frac{2}{3}z+\frac{1}{3} z=-5y+9$$

z=-5y+9 ह्या समिकरणांत y खातीर -\frac{2}{3}z+\frac{1}{3} बदलपी घेवचो.

$$z=-5\left(-\frac{2}{3}z+\frac{1}{3}\right)+9$$

z खातीर z=-5\left(-\frac{2}{3}z+\frac{1}{3}\right)+9 सोडोवचो.

$$z=-\frac{22}{7}$$

y=-\frac{2}{3}z+\frac{1}{3} ह्या समिकरणांत z खातीर -\frac{22}{7} बदलपी घेवचो.

$$y=-\frac{2}{3}\left(-\frac{22}{7}\right)+\frac{1}{3}$$

y=-\frac{2}{3}\left(-\frac{22}{7}\right)+\frac{1}{3} तल्यान y मेजचो.

$$y=\frac{17}{7}$$

y आनी -\frac{22}{7} ह्या समिकरणांत z खातीर \frac{17}{7} बदलपी घेवचो x=-y+z+2.

$$x=-\frac{17}{7}-\frac{22}{7}+2$$

x=-\frac{17}{7}-\frac{22}{7}+2 तल्यान x मेजचो.

$$x=-\frac{25}{7}$$

प्रणाली आतां सुटावी जाली.

$$x=-\frac{25}{7} y=\frac{17}{7} z=-\frac{22}{7}$$