Question
For what value of k, the pair of linear equations 3x+ky=9 and 6x+4y=18 has infinitely many solutions?
Answer: Option D
:
D
Given equations gives infinitely many solutions if,
a1a2=b1b2=c1c2
The given linear equations are:
3x+ky=9;6x+4y=18.
⇒a1=3,b1=k,c1=−9 and a2=6,b2=4,c2=−18
⇒36=k4=−9−18
⇒12=k4
⇒k=2
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:
D
Given equations gives infinitely many solutions if,
a1a2=b1b2=c1c2
The given linear equations are:
3x+ky=9;6x+4y=18.
⇒a1=3,b1=k,c1=−9 and a2=6,b2=4,c2=−18
⇒36=k4=−9−18
⇒12=k4
⇒k=2
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