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Q.
Find the equation of line parallel to the $y$-axis and drawn through the point of intersection of $x - 7y + 5 = 0$ and $3x + y - 7 = 0$
Straight Lines
Solution:
The equation of any line through the point of intersection of the given lines is of the form
$x - 7y + 5 + k (3x + y - 7) = 0$
i.e. $(1 + 3k)x + (k-7 )y + 5 - 7 k = 0 \quad \ldots(i)$
If this line is parallel to $y$-axis, then the coefficient of $y$ should be zero, i.e., $k - 7 = 0$ which gives $k = 7$.
Substituting this value of $k$ in the equation $(i)$,
we get $22x - 44 = 0$,
i.e., $x - 2 = 0$, which is the required equation.