If the given pair of equations has infinitely many solutions, then find the value of k?

$3 x + 4 y = k$
$15 x + 20 y = 35$

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Solution

The correct option is D 7
A pair of liner equations,

$a_{1} x + b_{1} y = c_{1}$
$a_{2} x + b_{2} y = c_{2}$

are said have infinitely many solutions if

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

$\Rightarrow \frac{3}{15} = \frac{4}{20} = \frac{k}{35}$

$\Rightarrow k = 7$

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