alleryStart learning →For what value of $k$ do the equations $2x+3y=7$ and $6x+9y=k$ have infinitely many solutions?
A7
B21
C14
D3
Answer & Solution
Correct answer: B. 21
1. Infinitely many solutions need $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$.
2. $\dfrac{2}{6}=\dfrac{3}{9}=\dfrac13$, so we need $\dfrac{7}{k}=\dfrac13$.
3. Thus $k=21$.
_Source: Karnataka SSLC (KSEEB) Class 10 Mathematics, Ch3 'Pair of Linear Equations in Two Variables', §3.2_
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