Question

The solution of the equation ax+by=1 and x=2 is (2,0) and that of ax+by=1 and y=3 is (0,3). Find a and b.

Answer 1

Intersection of 2x+3y−1=0,x+2y−1=0 is (−1,1).

Line passing through (−1,1) and origin is perpendicular to ax+by−1=0,

we get a=−b. ---1) using m

1

.m

2

=−1

Also, line passing through x+2y−1=0 and ax+by−1=0, is

x+2y−1+λ(ax+by−1)=0,

It passes through origin , so

λ=−1

Line is x(1−a)+y(2−b)=0

This is perpendicular to line 2x+3y−1=0

So, using m

1

.m

2

=−1 we get

2a+3b=8 ---2)

Then, on solving further, we get (a,b)=(8,−8)

hope it helps u mate....