Two lines $a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$ intersect at a unique point if

Two lines $a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$ intersect at a unique point if
  1. $\dfrac{a_1}{a_2} \ne \dfrac{b_1}{b_2}$
  2. $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2}$
  3. $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$
  4. $a_1 = a_2$

Solution

Different slopes $\Rightarrow$ unique intersection.

Asked in: MH-SSC-9

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