Question

13) p ਦੇ ਕਿਹੜੇ ਮੁੱਲਾਂ ਲਈ ਹੇਠ ਦਿੱਤੇ ਸਮੀਕਰਣ ਜੋੜੇ ਦਾ ਇੱਕ ਵਿਲੱਖਣ ਹੱਲ ਹੈ। For what values of p pair of linear eqations will have unique solution.
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Answer 1

Answer:

values of p other than 4.

Step-by-step explanation:

The given pair of linear equation :

⇒  (p+2)x−(2p+1)y=3(2p−1)                    ------ ( 1 )

⇒  2x−3y=7                             ------- ( 2 )

On comparing with equations,

a1​x+b1​y+c1​=0

and a2​x+b2​y+c2​=0

We get, a1​=(p+2),b1​=−(2p+1),c=−[3(2p−1)]

a2​=2,b2​=−3,c=−7

⇒  a2​a1​​=2p+2​ and b2​b1​​=−3−(2p+1)​

A pair of linear equations has a unique solution, if

⇒  a2​a1​​=b2​b1​​

⇒  2(p+2)​=−3−(2p+1​

⇒  −3(p+2)=2(−2p−1)

⇒  −3p−6=−4p−2

⇒  −3p+4p=−2+6

⇒  p=4

Therefore, the given system will have unique solution for all real values of p other than 4.