Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines

Here the equation of any line parallel to the y-axis is of the form

x = a ……. (1)

Two given lines are

x – 7y + 5 = 0 …… (2)

3x + y = 0 …… (3)

By solving equations (2) and (3) we get

x = \(- \dfrac{5}{22}\) and y = \( \dfrac{15}{22}\)

(\( - \dfrac{5}{22}\),\( \dfrac{15}{22}\)) is the point of intersection of lines (2) and (3)

If the line x = a passes through point (\( - \dfrac{5}{22}\), \( \dfrac{15}{22}\)) we get a = \( - \dfrac{5}{22}\)

Hence, the required equation of the line is x = \( - \dfrac{5}{22}\).