सोडोवचें {l}{2x-3y+z=12}{3x+4y-5z=9}{-x+2y+3z=15}

$$\left. \begin{array} { l } { 2 x - 3 y + z = 12 } \\ { 3 x + 4 y - 5 z = 9 } \\ { - x + 2 y + 3 z = 15 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x=8$$

$$y = \frac{35}{11} = 3\frac{2}{11} \approx 3.181818182$$

$$z = \frac{61}{11} = 5\frac{6}{11} \approx 5.545454545$$

बदली वापरून संक्षिप्त पांवडे

z खातीर 2x-3y+z=12 सोडोवचो.

$$z=-2x+3y+12$$

दुस-या आनी तिस-या समिकरणांत z खातीर -2x+3y+12 बदलपी घेवचो.

$$3x+4y-5\left(-2x+3y+12\right)=9 -x+2y+3\left(-2x+3y+12\right)=15$$

अनुक्रमान y आनी x खातीर हीं समिकरणां सोडोवचीं.

$$y=\frac{13}{11}x-\frac{69}{11} x=\frac{11}{7}y+3$$

x=\frac{11}{7}y+3 ह्या समिकरणांत y खातीर \frac{13}{11}x-\frac{69}{11} बदलपी घेवचो.

$$x=\frac{11}{7}\left(\frac{13}{11}x-\frac{69}{11}\right)+3$$

x खातीर x=\frac{11}{7}\left(\frac{13}{11}x-\frac{69}{11}\right)+3 सोडोवचो.

$$x=8$$

y=\frac{13}{11}x-\frac{69}{11} ह्या समिकरणांत x खातीर 8 बदलपी घेवचो.

$$y=\frac{13}{11}\times 8-\frac{69}{11}$$

y=\frac{13}{11}\times 8-\frac{69}{11} तल्यान y मेजचो.

$$y=\frac{35}{11}$$

y आनी 8 ह्या समिकरणांत x खातीर \frac{35}{11} बदलपी घेवचो z=-2x+3y+12.

$$z=-2\times 8+3\times \frac{35}{11}+12$$

z=-2\times 8+3\times \frac{35}{11}+12 तल्यान z मेजचो.

$$z=\frac{61}{11}$$

प्रणाली आतां सुटावी जाली.

$$x=8 y=\frac{35}{11} z=\frac{61}{11}$$