Question

Find the equation of the line joining the point (3, 5) to the point of intersection of the lines 4x + y − 1 = 0 and 7x − 3y − 35 = 0.

Answer 1

We have,
4x + y − 1 = 0         ... (1)
7x − 3y − 35 = 0     ... (2)
Solving (1) and (2) using cross-multiplication method:

\[\frac{x}{- 35 - 3} = \frac{y}{- 7 + 140} = \frac{1}{- 12 - 7}\]

\[ \Rightarrow x = 2, y = - 7\]

Thus, the point of intersection of the given lines is \[\left( 2, - 7 \right)\]. 

So, the equation of the line joining the points (3, 5) and \[\left( 2, - 7 \right)\] is

\[y - 5 = \frac{- 7 - 5}{2 - 3}\left( x - 3 \right)\]

\[ \Rightarrow y - 5 = 12x - 36\]

\[ \Rightarrow 12x - y - 31 = 0\]