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The number of the values of ' $k$ ' for which the lines $2 x+y=1,3 x+2 y=2, k x+3 y=3$ are concurrent is .........
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The correct answer is:
Infinity
It is given that the lines $2 x+y=1,3 x+2 y=2$ and $k x+3 y=3$ are concurrent, so
$$
\left|\begin{array}{ccc}
2 & 1 & -1 \\
3 & 2 & -2 \\
k & 3 & -3
\end{array}\right|=0
$$
$\because$ The elements of columns $C_2$ and $C_3$ are proportional to each other, so for any value of $k$ given lines are concurrent.
$$
\left|\begin{array}{ccc}
2 & 1 & -1 \\
3 & 2 & -2 \\
k & 3 & -3
\end{array}\right|=0
$$
$\because$ The elements of columns $C_2$ and $C_3$ are proportional to each other, so for any value of $k$ given lines are concurrent.
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