Question

Find the condition that the system of equations ax + by = c and lx + my = n has a unique solution ?

Answer 1

The given equations are : ax + by – c = 0 and lx + my – n = 0

Here, a₁ = a, b₁ = b, c₁ = –c, and a₂ = l, b₂ = m, c₂ = – n

For unique solution,

\(\frac{a_1}{a_2}\) \(\ne\) \(\frac{b_1}{b_2}\), i.e, \(\frac{a}{l}\)\(\ne\) \(\frac{b}{m}\) \(\Rightarrow\) am \(\ne\) bl