For a pair of linear equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$…

Question

For a pair of linear equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$, a unique solution exists when

Accepted Answer

A. $\dfrac{a_1}{a_2} 
e \dfrac{b_1}{b_2}$

1. The lines intersect (unique solution) when their slopes differ.
2. This happens when $\dfrac{a_1}{a_2} 
e \dfrac{b_1}{b_2}$.
3. (Equal ratios of all three give infinite solutions; equal a/b ratio but different c gives no solution.)
_Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.2_

Answer

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}
e\dfrac{c_1}{c_2}$

Answer

$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$

Answer

$a_1=a_2$ and $b_1=b_2$