the system of equations

4x+3y=9

2ax+(a+b)y=18

has infinitrely many solutions then prove a=2b

Hi!!

If it has many solution then it should satisfy a1/a2=b1/b2=c1/c2

or, 4/2a=3/a+b

or,4(a+b)=6a

or, a+b=3a/2----------(1)

now, 3/a+b=9/18

or, 3x2=a+b

or,6=a+b-------------(2)

Now from 1 and 2;

a+b=3a/2=6

or, a=4-------(3)

a+b=6

or,b=2----(4)

now a=4

and b=2

 so by combaring

a/b=4/2

or, a/b=2

or, a=2b proved