NIFT UG 2018 Question Paper with solutions

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Question : 21 of 150

Marks: +1, -0

For what value of

p,

the following pair of linear equations in two variables will have infinitely many solutions?

p x+3 y-(p-3)=0

12 x+p y-p=0

6
-6
0
2

Solution:

We have

p x+3 y-(p-3)=0

12 x+p y-p=0

For infinitely many solution of the equations

a_{1} x+b_{1} y+c_{1}=0

and

\;\; a_{2} x+b_{2} y+c_{2}=0

,

\;{a_{1}}/{a_{2}}=\;{b_{1}}/{b_{2}}=\;{c_{1}}/{c_{2}}

∴ \;\; \;{p}/{12}=\;{3}/{p}=\;{p-3}/{p}

⇒ \;\; \;{p}/{12}=\;{3}/{p} ⇒ p^{2}=36 ⇒ p=± 6

and

\;\; \;{3}/{p}=\;{p-3}/{p}

⇒ \;\; p-3=3 ⇒ p=6

Hence,

\;\; p=6

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