Question

For what value of k does the system of equations 2x + ky = 11 and 5x – 7y = 5 has no solution ?

Answer 1

The given equations are : 2x + ky – 11= 0 and 5x – 7y – 5 = 0

Here, a₁ = 2, b₁ = k, c₁ = -11 and a₂ = 5, b₂ = -7, c₂ = -5

The two equations will have no solution if,

\(\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}\), i.e., \(\frac{2}{5} = \frac{k}{-7}\ne\frac{-11}{-5}\)

\(\Rightarrow\) \(\frac{2}{5}\) = \(\frac{k}{-7}\) \(\Rightarrow\) k = \(\frac{-14}{5}\)