alleryFor the pair a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0, a unique solution exists when:
A$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}$
B$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$
C$a_1=a_2$
D$\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$
Answer & Solution
Correct answer: D. $\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$
a₁/a₂ ≠ b₁/b₂ gives intersecting lines and a unique solution.
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