सोडोवचें {l}{2x+y-z=9}{x-2y+z=-1}{x+2y+2z=-5}

$$\left. \begin{array}{l}{ 2 x + y - z = 9 }\\{ x - 2 y + z = - 1 }\\{ x + 2 y + 2 z = - 5 }\end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x = \frac{45}{17} = 2\frac{11}{17} \approx 2.647058824$$

$$y=-\frac{1}{17}\approx -0.058823529$$

$$z = -\frac{64}{17} = -3\frac{13}{17} \approx -3.764705882$$

बदली वापरून संक्षिप्त पांवडे

y खातीर 2x+y-z=9 सोडोवचो.

$$y=-2x+z+9$$

दुस-या आनी तिस-या समिकरणांत y खातीर -2x+z+9 बदलपी घेवचो.

$$x-2\left(-2x+z+9\right)+z=-1 x+2\left(-2x+z+9\right)+2z=-5$$

अनुक्रमान x आनी z खातीर हीं समिकरणां सोडोवचीं.

$$x=\frac{17}{5}+\frac{1}{5}z z=\frac{3}{4}x-\frac{23}{4}$$

z=\frac{3}{4}x-\frac{23}{4} ह्या समिकरणांत x खातीर \frac{17}{5}+\frac{1}{5}z बदलपी घेवचो.

$$z=\frac{3}{4}\left(\frac{17}{5}+\frac{1}{5}z\right)-\frac{23}{4}$$

z खातीर z=\frac{3}{4}\left(\frac{17}{5}+\frac{1}{5}z\right)-\frac{23}{4} सोडोवचो.

$$z=-\frac{64}{17}$$

x=\frac{17}{5}+\frac{1}{5}z ह्या समिकरणांत z खातीर -\frac{64}{17} बदलपी घेवचो.

$$x=\frac{17}{5}+\frac{1}{5}\left(-\frac{64}{17}\right)$$

x=\frac{17}{5}+\frac{1}{5}\left(-\frac{64}{17}\right) तल्यान x मेजचो.

$$x=\frac{45}{17}$$

x आनी -\frac{64}{17} ह्या समिकरणांत z खातीर \frac{45}{17} बदलपी घेवचो y=-2x+z+9.

$$y=-2\times \frac{45}{17}-\frac{64}{17}+9$$

y=-2\times \frac{45}{17}-\frac{64}{17}+9 तल्यान y मेजचो.

$$y=-\frac{1}{17}$$

प्रणाली आतां सुटावी जाली.

$$x=\frac{45}{17} y=-\frac{1}{17} z=-\frac{64}{17}$$