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

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 - 7k = 0                                   ... (1)

If this line is parallel to y-axis, then the coefficient of y should be zero, i.e.,

k - 7 = 0 ⇒ k = 7

Substituting this value of k in equation (1), we get

22x - 44 = 0

x - 2 = 0

Therefore, the required equation is x - 2 = 0.