If the point of intersection of lines $2 x + y = 7, 3 x + 2 y = 12,$ and $4 x + k y = 17$ have a common point of intersection, then find the value of k?

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Solution

The correct option is C 3
We have,
$2 x + y = 7$ .......(1)
$3 x + 2 y = 12$ ......(2)
Multiply equation (1) by 2, we get:
$\Rightarrow 2 (2 x + y) = 2 (7)$
$\Rightarrow 4 x + 2 y = 14$ ......(3)
Subract (2) from (3) we get
$\Rightarrow x = 2$
Substitute $x = 2$ in (1) we get
$\Rightarrow y = 7 - 2 (2)$
$\Rightarrow y = 3$
Thus, (2, 3) is the point of intersection of first two equation.
As the line $4 x + k y = 17$ passes through (2, 3),
$\Rightarrow 4 \times 2 + k \times 3 = 17$
$\Rightarrow 8 + 3 k = 17$
$3 k = 9$
$k = 3$

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