सोडोवचें {r}{2x+y-2z=-1}{3x-3y=5+z}{-2x+x+3z=5}

$$\left\{ \begin{array} { r } { 2 x + y - 2 z = - 1 } \\ { 3 x - 3 y = 5 + z } \\ { - 2 x + x + 3 z = 5 } \end{array} \right.$$

x, y, z खातीर सोडोवचें

$$x = \frac{41}{20} = 2\frac{1}{20} = 2.05$$

$$y=-\frac{2}{5}=-0.4$$

$$z = \frac{47}{20} = 2\frac{7}{20} = 2.35$$

बदली वापरून संक्षिप्त पांवडे

y खातीर 2x+y-2z=-1 सोडोवचो.

$$y=-2x+2z-1$$

3x-3y=5+z ह्या समिकरणांत y खातीर -2x+2z-1 बदलपी घेवचो.

$$3x-3\left(-2x+2z-1\right)=5+z$$

x खातीर दुसरें समिकरण आनी z खातीर तिसरें समिकरण सोडोवचें.

$$x=\frac{7}{9}z+\frac{2}{9} z=\frac{5}{3}+\frac{1}{3}x$$

z=\frac{5}{3}+\frac{1}{3}x ह्या समिकरणांत x खातीर \frac{7}{9}z+\frac{2}{9} बदलपी घेवचो.

$$z=\frac{5}{3}+\frac{1}{3}\left(\frac{7}{9}z+\frac{2}{9}\right)$$

z खातीर z=\frac{5}{3}+\frac{1}{3}\left(\frac{7}{9}z+\frac{2}{9}\right) सोडोवचो.

$$z=\frac{47}{20}$$

x=\frac{7}{9}z+\frac{2}{9} ह्या समिकरणांत z खातीर \frac{47}{20} बदलपी घेवचो.

$$x=\frac{7}{9}\times \frac{47}{20}+\frac{2}{9}$$

x=\frac{7}{9}\times \frac{47}{20}+\frac{2}{9} तल्यान x मेजचो.

$$x=\frac{41}{20}$$

x आनी \frac{47}{20} ह्या समिकरणांत z खातीर \frac{41}{20} बदलपी घेवचो y=-2x+2z-1.

$$y=-2\times \frac{41}{20}+2\times \frac{47}{20}-1$$

y=-2\times \frac{41}{20}+2\times \frac{47}{20}-1 तल्यान y मेजचो.

$$y=-\frac{2}{5}$$

प्रणाली आतां सुटावी जाली.

$$x=\frac{41}{20} y=-\frac{2}{5} z=\frac{47}{20}$$