Question

9. Find the value of p for which the following pair
of equations has infinitely many solutions :
2x + 3y = 7 and 2px + py = -28 - qy.
(a) - 4
(b) 2
(c)-2
(d) 3​

Answer 1

Answer: p = - 4.

Explanation:

First equation: 2x + 3y - 7 = 0

Rewriting 2px + py = - 28 - qy as 2px + (p + q)y + 28 = 0.

For infinitely many solutions,

$\rm \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$.

So, 2/2p = 3/(p + q) = - 7/28

⇒ 1/p = - 1/4

⇒ p = - 4 (a).

More: Equations having infinitely many solutions or even a single solution are called consistent pairs. For those equations which have no solutions, it is called inconsistent pair.

• In case of no solution, $\rm \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$.
• And in case of one solution, $\rm \dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$.