For what value of k , the following pair of linear equations has infinite number of solutions :
$5 x + 2 y = k; 10 x + 4 y = 3$

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Solution

The given equations are :

$5 x + 2 y - k = 0$

$10 x + 4 y - 3 = 0$

For infinitely many solutions,

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

Therefore,

$\frac{5}{10} = \frac{2}{4} = \frac{- k}{- 3}$

$\frac{k}{3} = \frac{1}{2}$

$k = \frac{3}{2}$

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