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# Find the equation of the line parallel to $y$ - axis and drawn through the point of intersection of the lines $x – 7y + 5 = 0$ and $3x + y = \theta.$

$\begin {array} {1 1} (A)\;x = \large\frac{5}{22} & \quad (B)\;x=-\large\frac{5}{22} \\ (C)\;y = \large\frac{5}{22} & \quad (D)\;y =- \large\frac{5}{22} \end {array}$

Toolbox:
• Equation of a line passing parallel to $y$ - axis is $x=a$, where $a$ is a constant.
Given equation of the two lines are
$\qquad x-7y+5=0$
$\qquad 3x+y=0$
On solving the two equations for $x$ and $y$ we get,
$\qquad x-7(-3x)+5=0$
$\qquad 22x+5=0 \Rightarrow x = - \large\frac{5}{22}$
and $y = \large\frac{15}{22}$
The point of intersection of the above two lines is $\bigg( -\large\frac{5}{22}$$, \large\frac{15}{22} \bigg) Since the line x=a passes through the point \bigg( -\large\frac{5}{22}$$, \large\frac{15}{22} \bigg)$
$a = -\large\frac{5}{22}$
Hence the required equation of the line is
$x = -\large\frac{5}{22}$