The pair of linear equations $4 x + 6 y = 9 a n d 2 x + 3 y = 6$ has

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Solution

The correct option is B No solution
Given system of linear equations
$4 x + 6 y - 9 = 0 \Rightarrow a_{1} = 4, b_{1} = 6, c_{1} = - 9$
$2 x + 3 y - 6 = 0 \Rightarrow a_{2} = 2, b_{2} = 3, c_{2} = - 6$ .

As we know a pair of linear equations is inconsistent (no solution) if
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
We have $\frac{4}{2} = \frac{6}{3} \neq \frac{- 9}{- 6}$
Hence, no solution.

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