For all real values of $c$ , the pair of equations $x - 2 y = 8, 5 x + 10 y = c$ have a unique solution?

True

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False

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Solution

The correct option is A True
True
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, $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
So, for all real values of $c$ , the given pair of equations have a unique solution.

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Similar questions

Determine the value of k for which the given system of equations has a unique solution:
$x - k y = 2, 3 x + 2 y = - 5$

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