Question

If the equations 4x + 7y = 10 and 10x + ky = 25 represent coincident lines, then find the value of k ?

Answer 1

The given equations are : 4x + 7y – 10 = 0 and 10x + ky – 25 = 0 

Here, a₁ = 4, b₁ = 7, c₁ = –10 

a₂ = 10, b₂ = k, c₂ = – 25 

For the given equation to represent coincident lines, 

\(\frac{a_1}{a_2}\)=\(\frac{b_1}{b_2}\)=\(\frac{c_1}{c_2}\) i.e., \(\frac{4}{10}\) = \(\frac{7}{k}\) = \(\frac{-10}{-25}\)

\(\Rightarrow\) \(\frac{4}{10}\) = \(\frac{7}{k}\) \(\Rightarrow\) \(\frac{70}{4}\) = \(\frac{35}{2}\)