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Question

For what value of k, will the following pair of linear equations in two variable have infinitely many solutions?

2x+3y=4,(k+2)x+6y=3k+2

A
k = 2
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B
k = 3
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C
k = 4
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D
k = 5
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Solution

The correct option is A k = 2
Given: 2x+3y=4,(k+2)x+6y=3k+2

Condition for infinitely many solutions is

a1a2=b1b2=c1c2

a1=2,a2=k+2, b1=3,b2=6, c1=4, c2=(3k+2)


2k+2=36=4(3k+2)

2k+2=36

2k+2=12

k+2=4

k=2

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