सोडोवचें {l}{150=9/4a+3/2b+c}{45=25a+5b+c}{225/2=4a+2b+c}

$$\left\{ \begin{array} { l } { 150 = \frac { 9 } { 4 } a + \frac { 3 } { 2 } b + c } \\ { 45 = 25 a + 5 b + c } \\ { \frac { 225 } { 2 } = 4 a + 2 b + c } \end{array} \right.$$

a, b, c खातीर सोडोवचें

$$a=15$$

$$b = -\frac{255}{2} = -127\frac{1}{2} = -127.5$$

$$c = \frac{615}{2} = 307\frac{1}{2} = 307.5$$

बदली वापरून संक्षिप्त पांवडे

c खातीर 150=\frac{9}{4}a+\frac{3}{2}b+c सोडोवचो.

$$c=150-\frac{9}{4}a-\frac{3}{2}b$$

दुस-या आनी तिस-या समिकरणांत c खातीर 150-\frac{9}{4}a-\frac{3}{2}b बदलपी घेवचो.

$$45=25a+5b+150-\frac{9}{4}a-\frac{3}{2}b \frac{225}{2}=4a+2b+150-\frac{9}{4}a-\frac{3}{2}b$$

अनुक्रमान b आनी a खातीर हीं समिकरणां सोडोवचीं.

$$b=-30-\frac{13}{2}a a=-\frac{150}{7}-\frac{2}{7}b$$

a=-\frac{150}{7}-\frac{2}{7}b ह्या समिकरणांत b खातीर -30-\frac{13}{2}a बदलपी घेवचो.

$$a=-\frac{150}{7}-\frac{2}{7}\left(-30-\frac{13}{2}a\right)$$

a खातीर a=-\frac{150}{7}-\frac{2}{7}\left(-30-\frac{13}{2}a\right) सोडोवचो.

$$a=15$$

b=-30-\frac{13}{2}a ह्या समिकरणांत a खातीर 15 बदलपी घेवचो.

$$b=-30-\frac{13}{2}\times 15$$

b=-30-\frac{13}{2}\times 15 तल्यान b मेजचो.

$$b=-\frac{255}{2}$$

b आनी 15 ह्या समिकरणांत a खातीर -\frac{255}{2} बदलपी घेवचो c=150-\frac{9}{4}a-\frac{3}{2}b.

$$c=150-\frac{9}{4}\times 15-\frac{3}{2}\left(-\frac{255}{2}\right)$$

c=150-\frac{9}{4}\times 15-\frac{3}{2}\left(-\frac{255}{2}\right) तल्यान c मेजचो.

$$c=\frac{615}{2}$$

प्रणाली आतां सुटावी जाली.

$$a=15 b=-\frac{255}{2} c=\frac{615}{2}$$