The pair of linear equations 2x+5y=k, kx+15y=18 has infinitely many solutions if

The given pair of linear equations are,

2 x + 5 y = k

kx + 15 y = 18

Here,

a_{1} = 2, b_{1} = 5, c_{1} = - k

.
And

a_{2} = k, b_{2} = 15, c_{2} = - 18

.
The system of equation has infinitely many solutions if

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

\Rightarrow \frac{2}{k} = \frac{5}{15} = \frac{- k}{- 18}

\Rightarrow \frac{2}{k} = \frac{1}{3} = \frac{k}{18}

Taking,
⇒

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

\Rightarrow k = 6

Taking,
⇒

\frac{1}{3} = \frac{k}{18}

⇒

k = 6

Hence, the correct option is 2.

The pair of linear equations $2 x + 5 y = k, kx + 15 y = 18$ has infinitely many solutions if