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Question

Which of the following pair of linear equations has infinite solutions?


A

x+2y=7; 3x+6y=21

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B

4x+3y=7; 3x+6y=25

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C

y+2x=10; 11x+6y=21

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D

12x+2y=711; x+6y=21

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Solution

The correct option is A

x+2y=7; 3x+6y=21


If two equations are consistent and overlapping, then they will have infinite solutions. Option A consists of two equations where the second equation can be reduced to an equation which is same as the first equation.
x+2y=7 ....(i)
3x+6y=21 .....(ii)
Dividing equation (ii) by 3, we get
x+2y=7 which is the same as equation (i).
The equations coincide and will have an infinite solution.
Alternate Method:
Let the two equations be
a1x+b1y+c1=0
a2x+b2y+c2=0
The condition for having infinite solutions is:
a1a2=b1b2=c1c2 ...(i)
For the equations , on substituting values in eq (i), we get
13=26=721
The pair of equations x+2y=7 and 3x+6y=21 . have infinite solutions.
Similarly, we can check that other options don't have infinite solutions.


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