Correct option is: (B) inconsistent
\(6 x-3 y+10=0 \) .....(i)
\( 2 x-y+9=0 \) .....(ii)
\(6 x-3 y+10=0\)
Comparing with \(a_1 x+b_1 y+c_1=0\)
\( a_1=6, b_1=-3, \ c_1=10 \)
2x - y + 9 = 0
Comparing with \(a_2 x+b_2 y+c_2=0\)
\(a_2=2,\ b_2=-1, \ c_2=9 \)
\( \frac{a_1}{a_2}=\frac{6}{2}=3 \)
\(\frac{b_1}{b_2}=\frac{-3}{-1}=3 \)
\( \frac{c_1}{c_2}=\frac{10}{9}\)
Since, \( \frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)
So, we have no solution
Therefore, the lines represent the linear equations are parallel.
