How would I solve A*B = 2 and A+B = 3 without substituting values?

Question

I know that the answers are 1 and 2, and I got those from inputting those values into both equations. Is there any other way of solving for A and B?

Answer 1

Well if you are not allowed to use substitution, then the only other option is elimination.

Multiplies the second equation by B: AB + B^2 = 3B

AB =2

subtracts them: B^2 = 3b - 2

B^2 - 3b + 2= 0

( b - 1)( b - 2 ) = 0

b = 1 or b=2

for b=1 --> a = 2

for b=2 -->a=1