UPSC NDA I 2015 Mathematics Solved Paper

The intersection point for the lines can be found as follows,
ax+by=ab...(1)
bx+ay=ab...(2)
(b×1)−(a×2)→
abx+b2y−abx−a2y=ab2−a2b
⇒(b2−a2)y=ab(b−a)
y=

ab

a+b

∴x=

ab

a+b

Hence, slope of the line passing through the origin and the point of intersection of the above two lines will be given by
m=

ab a+b ab

a+b

=1
∴ Equation of the line is y=x