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How many solutions does the following system of equations have
$3 x - 6 y = 9, 2 y - 4 x = 6$ ?

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1

2

4

Infinite

answer is D.

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Detailed Solution

The given equations can be written as:

3 x - 6 y = 9

— (|)

2 y - 4 x = 6

— (||)
Divide eq (|) and (||) by

3 and 2

respectively

y - 2 x = 3

— (|||)

y - 2 x = 3

— (IV)
Equation (III) and (IV) are identical and denote the same line.
So,

x = x_{1}

, So,

y_{1} = 2 x_{1} + 3

Here,

(x_{1}, y_{1})

is a solution to the equation and there is infinite

(x_{1}, y_{1})

lying on the line

y = 2 x + 3 .

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