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Question

Find the value of a and b for which the following system of linear equations has infinitely many solutions.

(aāˆ’1)x+3y=26x+(1āˆ’2b)y=6

A

3 and -4
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B

4 and -3
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C

2 and 1
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D

7 and 4
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Solution

The correct option is A
3 and -4
(a1)x+3y=2...(1)6x+(12b)y=6.....(2)

For infinitely many solutions, we must have

a1a2=b1b2=c1c2a16=312b=26a16=26a1=2a=2+1a=3And, 312b=269=12b2b=192b=8b=82b=4

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