सोडोवचें {l}{3x+2y+z=11}{2x+3y+2z=11}{4x+3y+3z=11}

$$\left\{ \begin{array} { l } { 3 x + 2 y + z = 11 } \\ { 2 x + 3 y + 2 z = 11 } \\ { 4 x + 3 y + 3 z = 11 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x = \frac{11}{7} = 1\frac{4}{7} \approx 1.571428571$$

$$y = \frac{33}{7} = 4\frac{5}{7} \approx 4.714285714$$

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

बदली वापरून संक्षिप्त पांवडे

z खातीर 3x+2y+z=11 सोडोवचो.

$$z=-3x-2y+11$$

दुस-या आनी तिस-या समिकरणांत z खातीर -3x-2y+11 बदलपी घेवचो.

$$2x+3y+2\left(-3x-2y+11\right)=11 4x+3y+3\left(-3x-2y+11\right)=11$$

अनुक्रमान y आनी x खातीर हीं समिकरणां सोडोवचीं.

$$y=-4x+11 x=-\frac{3}{5}y+\frac{22}{5}$$

x=-\frac{3}{5}y+\frac{22}{5} ह्या समिकरणांत y खातीर -4x+11 बदलपी घेवचो.

$$x=-\frac{3}{5}\left(-4x+11\right)+\frac{22}{5}$$

x खातीर x=-\frac{3}{5}\left(-4x+11\right)+\frac{22}{5} सोडोवचो.

$$x=\frac{11}{7}$$

y=-4x+11 ह्या समिकरणांत x खातीर \frac{11}{7} बदलपी घेवचो.

$$y=-4\times \frac{11}{7}+11$$

y=-4\times \frac{11}{7}+11 तल्यान y मेजचो.

$$y=\frac{33}{7}$$

y आनी \frac{11}{7} ह्या समिकरणांत x खातीर \frac{33}{7} बदलपी घेवचो z=-3x-2y+11.

$$z=-3\times \frac{11}{7}-2\times \frac{33}{7}+11$$

z=-3\times \frac{11}{7}-2\times \frac{33}{7}+11 तल्यान z मेजचो.

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

प्रणाली आतां सुटावी जाली.

$$x=\frac{11}{7} y=\frac{33}{7} z=-\frac{22}{7}$$