Question:
Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines $x-7 y+5=0$ and $3 x+y=0$.
Solution:
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, $\left(-\frac{5}{22}, \frac{15}{22}\right)$ is the point of intersection of lines (2) and (3).
Since line $x=$ a passes through point $\left(-\frac{5}{22}, \frac{15}{22}\right), a=-\frac{5}{22}$.
Thus, the required equation of the line is $x=-\frac{5}{22}$.