सोडोवचें {l}{-17x+7y-7z=505}{7x+4y+2z=-65}{19x+2y+8z=-369}

$$\left. \begin{array}{l}{ - 17 x + 7 y - 7 z = 505 }\\{ 7 x + 4 y + 2 z = - 65 }\\{ 19 x + 2 y + 8 z = - 369 }\end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x=-19$$

$$y=20$$

$$z=-6$$

बदली वापरून संक्षिप्त पांवडे

x खातीर -17x+7y-7z=505 सोडोवचो.

$$x=\frac{7}{17}y-\frac{7}{17}z-\frac{505}{17}$$

दुस-या आनी तिस-या समिकरणांत x खातीर \frac{7}{17}y-\frac{7}{17}z-\frac{505}{17} बदलपी घेवचो.

$$7\left(\frac{7}{17}y-\frac{7}{17}z-\frac{505}{17}\right)+4y+2z=-65 19\left(\frac{7}{17}y-\frac{7}{17}z-\frac{505}{17}\right)+2y+8z=-369$$

अनुक्रमान y आनी z खातीर हीं समिकरणां सोडोवचीं.

$$y=\frac{270}{13}+\frac{5}{39}z z=\frac{3322}{3}-\frac{167}{3}y$$

z=\frac{3322}{3}-\frac{167}{3}y ह्या समिकरणांत y खातीर \frac{270}{13}+\frac{5}{39}z बदलपी घेवचो.

$$z=\frac{3322}{3}-\frac{167}{3}\left(\frac{270}{13}+\frac{5}{39}z\right)$$

z खातीर z=\frac{3322}{3}-\frac{167}{3}\left(\frac{270}{13}+\frac{5}{39}z\right) सोडोवचो.

$$z=-6$$

y=\frac{270}{13}+\frac{5}{39}z ह्या समिकरणांत z खातीर -6 बदलपी घेवचो.

$$y=\frac{270}{13}+\frac{5}{39}\left(-6\right)$$

y=\frac{270}{13}+\frac{5}{39}\left(-6\right) तल्यान y मेजचो.

$$y=20$$

y आनी -6 ह्या समिकरणांत z खातीर 20 बदलपी घेवचो x=\frac{7}{17}y-\frac{7}{17}z-\frac{505}{17}.

$$x=\frac{7}{17}\times 20-\frac{7}{17}\left(-6\right)-\frac{505}{17}$$

x=\frac{7}{17}\times 20-\frac{7}{17}\left(-6\right)-\frac{505}{17} तल्यान x मेजचो.

$$x=-19$$

प्रणाली आतां सुटावी जाली.

$$x=-19 y=20 z=-6$$