Find the equation of line joining the point (3, 5) to the point of intersection of the lines 4x + y - 1 = 0 and 7x - 3y

Solution :

On solving the equations 4x + y – 1 = 0 and 7x – 3y – 35 = 0 by using point of intersection formula, we get

x = 2 and y = -7

So, given lines intersect at (2, -7)

Now, the equation of line joining the point (3, 5) and (2, -7) is

\(\implies\) y – 5 = \(-7 – 5\over 2 – 3\)(x – 3)

\(\implies\) y – 5 = 12x – 36 \(\implies\) 12x – y – 31 = 0

is the required equation of line.