For each real value of $c$ , the pair of equations $x - 2 y = 8; 5 x - 10 y = c$ has a unique solution. Justify whether it is True or False.

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Solution

$x - 2 y = 8$
$5 x - 10 y = c$
Here $\frac{a_{1}}{a_{2}} = \frac{1}{5}, \frac{b_{1}}{b_{2}} = \frac{- 2}{- 10} = \frac{1}{5}, \frac{c_{1}}{c_{2}} = \frac{8}{c}$
Since $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}$
Therefore it cannot have unique solution for any value of $c$
Hence, The given statement is false.

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