If the system of equations kx − 5y = 2, 6x + 2y = 7

The given systems of equations are

$k x-5 y=2$

$6 x+2 y=7$

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

Here $a_{1}=k, a_{2}=6, b_{1}=-5, b_{2}=2$

$\frac{k}{6}=\frac{-5}{2}$

$k=\frac{-30}{2}$

$k=-15$

Hence, the correct choice is $d$.