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Question

Find the value of a and b for which the system
2x+3y=7
(a+b)x+(2ab)y=3(a+b+1)
will have infinite number of solutions

A
a=5,b=2
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B
a=3,b=1
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C
a=5,b=1
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D
None
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Solution

The correct option is C a=5,b=1
Equations have infinite number of solutions, when both the equations are same.
a+b2=2ab3=3(a+b+1)7
Now,
a+b2=2ab3
=>3a+3b=4a2b
a=5b
Also, a+b2=3(a+b+1)7
7a+7b=6a+6b+6
a+b=6
=>5b+b=6
=>6b=6
=>b=1
And a=5b=5

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