Question

Find the equation of the straight line passing through the point (2, 0) and through the point of intersection of the lines x + 2y = 3 and 2x − 3y = 4.

Answer 1

The equation of any straight line passing through the intersection of the lines x + 2y = 3 and 2x − 3y − 4 = 0  is written as

λ(x + 2y − 3) + (2x − 3y − 4) = 0 ..... (1)

Since the line passes through the point (2, 0), we have 

λ(2 + 0 − 3) + (4 − 0 − 4) = 0 

That is, λ = 0. Now substituting this value of λ in Eq. (1), we get 

2x − 3y − 4 = 0

which is the equation of the given line.