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Question

The pair of linear equations 13x+ky=k and 39x+6y=k+4 has infinitely many solutions if:

A
k = 1
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B
k = 2
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C
k = 4
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D
k = 6
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Solution

The correct option is B k = 2
The pair of linear equations, 13x+kyk=0 and 39x+6y(k+4)=0 has infinitely many solutions if:

a1a2=b1b2=c1c2

1339=k6=k(k+4)

13=k6=kk+4

Equating the 1st and 2nd part of the above equation we get,

13=k6

k=2

OR

Equating the 1st and 3rd part of the above equation we get,

13=kk+4

k+4=3k
2k=4
k=2

When k = 2, the pair of linear equations has infinite solutions.

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