alleryStart learning →The pair of equations $2x+3y=5$ and $4x+6y=10$ has
Aa unique solution
Binfinitely many solutions
Cno solution
Dexactly one solution
Answer & Solution
Correct answer: B. infinitely many solutions
1. Compare ratios: $\dfrac{a_1}{a_2}=\dfrac{2}{4}=\dfrac12$, $\dfrac{b_1}{b_2}=\dfrac{3}{6}=\dfrac12$, $\dfrac{c_1}{c_2}=\dfrac{5}{10}=\dfrac12$.
2. All three ratios are equal, so the lines are coincident.
3. Hence there are **infinitely many solutions**.
_Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.2_
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