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

Condition for infinitely many solutions is:

a1a2=b1b2=c1c2

a1=2, a2=6, b1=3, b2=k

26=3kk=9

When k=9, it represents two exactly same lines, so all the points coincide, thus giving infinitely many solutions.

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