Answer:
k = -9
Step-by-step explanation:
The equations are of the form
ax+by+c=0
Two equations have no solution when
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]
3x-2y-12=0 ; kx+6y-10=0
[tex]\frac{3}{k}=\frac{-2}{6}\\\Rightarrow k=3\times \frac{6}{-2}\\\Rightarrow k=-9[/tex]
[tex]\frac{c_1}{c_2}=\frac{-12}{-10}=1.2[/tex]
So,
[tex]\frac{3}{-9}=\frac{-2}{6}\neq 1.2[/tex]
Hence, k = -9
