If the system of equation $a x + y = 3, x + 2 y = 3, 3 x + 4 y = 7$ is consistent, then value of $a$ is given by

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Solution

The correct option is C $1$
If system of given equation is consistent then they will intersect at a point.
Point of intersection of $x + 2 y = 3$ and $3 x + 4 y = 7$ is $(1, 2)$
Now this point will also satisfy $a x + y = 3$
$\Rightarrow a + 2 = 3 \Rightarrow a = 3 - 2 = 1$

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