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Q.

How many solutions does the following system of equations have

3x-6y=9, 2y-4x=6?

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a

1

b

2

c

4

d

Infinite 

answer is D.

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Detailed Solution

The given equations can be written as:
3x-6y=9      — (|)
2y-4x=6      — (||)
Divide eq (|) and (||) by 3 and 2 respectively
y-2x=3      — (|||)
y-2x=3      — (IV)
Equation (III) and (IV) are identical and denote the same line.
So, x=x1, So,
y1=2x1+3
Here, x1,y1 is a solution to the equation and there is infinite x1,y1 lying on the line y=2x+3.
     
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