For which value of the k, the pair of linear equations has no solution \(6x-3y+10=0\) and \(kx-y+9=0\):
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
Two linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) have no solution when their lines are parallel, that is, when \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne\frac{c_1}{c_2}\).
\(\frac{6}{k}=\frac{-3}{-1}=3\), so \(k=2\)
For \(k=2\), \(\frac{c_1}{c_2}=\frac{10}{9}\), which is not 3, so the lines are parallel and do not meet