Question

For what value of k will the given equations in two variables represent coincident lines : 2x + 32y + 3 = 0 and 3x + 48y + k = 0 ?

(a) \(\frac{2}{3}\)

(b) \(\frac{3}{2}\)

(c) \(\frac{9}{2}\)

(d) 1

Answer 1

(c) \(\frac{9}{2}\)

Here, a₁ = 2, b₁ = 32, c₁ = 3 

a₂ = 3, b₂ = 48, c₂ = k

For coincident lines,

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

\(\Rightarrow\)\(\frac{2}{3}\) = \(\frac{32}{48}\) = \(\frac{3}{k}\)

\(\Rightarrow\)\(\frac{3}{k}\)= \(\frac{2}{3}\)

\(\Rightarrow\) 2k = 9

\(\Rightarrow\) k = \(\frac{9}{2}\)