Find the equation of the straight line passing through the point (2, 1) and through the point of intersection of the lines x + 2y = 3 and 2x – 3y= 4.
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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 E. (1), we get 2x − 3y − 4 = 0
which is the equation of the given line.
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