Question

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 $3x + y = 0.$

Answer 1

The equation of any line parallel to the y-axis is of the form
$x = a … (1)$
The two given lines are
$x \- 7y + 5 = 0 … (2)$
$3x + y = 0 … (3)$
On solving equations (2) and (3), we obtain

$x = \frac{-5}{22}$ and $y = \frac{15}{22}$

Therefore$,(\frac{-5}{22},\frac{15}{22})$ is the point of intersection of lines (2) and (3).
Since line $x = a$ passes through point $(\frac{-5}{22},\frac{15}{22})$, $a=\frac{-5}{22}$

Thus, the required equation of the line is $x=\frac{-5}{22}.$