alleryIf $a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$ have a unique solution, which condition must hold true?
A$a_1/a_2 \ne b_1/b_2$
B$a_1/a_2 = b_1/b_2 \ne c_1/c_2$
C$a_1/a_2 = b_1/b_2 = c_1/c_2$
D$a_1 b_1 = a_2 b_2$
Answer & Solution
Correct answer: A. $a_1/a_2 \ne b_1/b_2$
1. A pair of linear equations has a unique solution if and only if the lines intersect at exactly one point.
2. The condition for intersecting lines is that their ratios are unequal: $a_1/a_2 \ne b_1/b_2$.
_Source: NCERT Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables'_
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