MathematicsThe pair of linear equations 3x+5y=3, 6x+ky=8 do not have any solution if

The pair of linear equations $3 x + 5 y = 3, 6 x + ky = 8$ do not have any solution if

The given equation are,

3 x + 5 y - 3 = 0

....(1)

6 x + ky - 8 = 0

....(2)
Here,

a_{1} = 3, b_{1} = 5, c_{1} = - 3

.
And

a_{2} = 6, b_{2} = k, c_{2} = - 8

.
The given system has no solution if

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

\Rightarrow \frac{3}{6} = \frac{5}{k} \neq \frac{- 3}{- 8}

\Rightarrow 3 k = 30

\Rightarrow k = 10

Hence, the correct option is 2.

JEE