Find the values of p and q for which the following system of equations has infinite number of
solutions:2x+3y=7(p+ q) x + (2p q) y =21

Open in App

Solution

$G i v e n s y s t e m o f e q u a t i o n s a r e 2 x + 3 y = 7 a n d (p + q) x + (2 p - q) y = 21 w e c a n w r i t e i t a s 2 x + 3 y - 7 = 0 a n d (p + q) x + (2 p - q) y - 21 = 0 H e r e a_{1} = 2, b_{1} = 3, c_{1} = - 7 a n d a_{2} = (p + q), b_{2} = (2 p - q), c_{2} = - 21 T h e g i v e n s y s t e m o f e q u a t i o n h a s i n f i n i t e l y m a n y s o l u t i o n s ∴ \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} \Rightarrow \frac{2}{(p + q)} = \frac{3}{(2 p - q)} = \frac{- 7}{- 21} ∴ \frac{2}{(p + q)} = \frac{1}{3} \Rightarrow p + q = 6 . . . . . . . . (1) \frac{3}{(2 p - q)} = \frac{1}{3} \Rightarrow 2 p - q = 9 . . . . . . . (2) S o l v i n g (1) a n d (2) . w e g e t 2 p - (6 - p) = 9 (u \sin g (1)) \Rightarrow 2 p - 6 + p = 9 \Rightarrow 3 p = 15 \Rightarrow p = 5 P u t t i n g t h e v a l u e o f p w e g e t q = 1 H e n c e t h e v a l u e s o f p a n d q a r e 5 a n d 1 r e s p e c t i v e l y$

Suggest Corrections

Similar questions

2 x + 3 y = 7

(p + q) x + (2 p - q) y = 21

x + y + z = 4

2 x + y + 3 z = 6

x + 2 y + p z = q

p = p^{'}

q = q^{'},

(p^{'})^{2} + (q^{'})^{2}

Find the values of a and b for which rach of the following systems of linear equations has an infinite number of equations:

$2 x + 3 y = 7, (a + b) x + (2 a - b) y = 21.$

2 x + 3 y = 7 (a + b) x + (2 a - b) y = 21

Join BYJU'S Learning Program