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

Solution :

On solving the equations x – 7y + 5 = 0 and 3x + y = 0 by using point of intersection formula, we get

x = \(-5\over 22\) and y = \(15\over 22\)

So, given lines intersect at \(({-5\over 22}., {15\over 22})\)

Let the equation of the required line be

x = \(\lambda\) ……….(i)

because the equation of a line parallel to y-axis is x = constant.

Since, equation (i) passes through \(({-5\over 22}., {15\over 22})\)

\(\therefore\) \(\lambda\) = \(-5\over 22\)

Substituting the value of \(\lambda\) in equation (i), we get

x = \(-5\over 22\) or, 22x + 5 = 0

as the equation of the required line.