alleryStart learning →The pair of equations $x+2y=4$ and $2x+4y=12$ has
Aa unique solution
Binfinitely many solutions
Cno solution
Dtwo solutions
Answer & Solution
Correct answer: C. no solution
1. Ratios: $\dfrac{a_1}{a_2}=\dfrac12$, $\dfrac{b_1}{b_2}=\dfrac24=\dfrac12$, $\dfrac{c_1}{c_2}=\dfrac{4}{12}=\dfrac13$.
2. Here $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\ne\dfrac{c_1}{c_2}$, so the lines are parallel.
3. Therefore the pair has **no solution**.
_Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.2_
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