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Question

Find the value of k for which following system of equations have infinitely many solutions
2x+3y5=0
6x+ky15=0


A
k = 9
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B
k = 2
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C
k = 3
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D
k = 4
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Solution

The correct option is A k = 9

Condition for infinitely many solutions is

a1a2=b1b2=c1c2
Given lines:

2x+3y5=0
6x+ky15=0

26=3kk=9

When k=9, it represents the same line, therefore all the points coincide, thus giving infinitely many solutions.


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