Question

Find values of a and b. 2x-3y=7. (a+b)x - (a+b-3)y=4a+b.

Answer 1

Here,a₁=2, b₁=3 and c₁=7

a₂=a+b, b₂=a+b-3 and c₂=4a+b

Now, for infinite number of solution,

a1/a2=b1/b2

=>2/a+b=3/a+b-3

=> 2a+ab-6=3a+3b

=> a+b+6=0

=> a=(-b-6) -----(1)

Also,b1/b2=c1/c2

3/a+b-3=7/4a+b

=> 7a+7b-21=12a+3b

=> 5a-4b+21=0

From (1),

5(-b-6)-4b+21=0

=> -5b-30-4b+21=0

=> -9b=9

=>b= -1

Now,a=(-b-6)= [-(-1)-6]=1-6= -5

Therefore value of a is -5 and b is -1