# 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.

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