If the system of equations 2x+5y= 7,6x+λ y= 28 is inconsistent, then

The correct answer is Option (4) → \(\lambda=15\)

Two equations \(a_1x + b_1y = c_1\) and \(a_2x + b_2y = c_2\) are inconsistent (parallel lines) when

    \( \displaystyle \frac{a_1}{a_2} = \frac{b_1}{b_2} \ne \frac{c_1}{c_2} \)

Here

    \( \displaystyle \frac{2}{6} = \frac{5}{\lambda} \)

    \(2\lambda = 30\)
\(\lambda = 15\)

The ratio of the constants is different:

    \( \displaystyle \frac{7}{28} = \frac{1}{4} \ne \frac{1}{3} \)

So the system is inconsistent for \(\lambda = 15\). For \(\lambda \ne 15\) it has a unique solution.