Solutions to systems of equations

[kent davidge]

The set of equations $$A = a_1 x + a_2y$$ ¨$$B = b_1 x + b_2 y$$ can be solved for the unkowns $x$ and $y$. Does it make sense to have $x$ and $y$ be known and instead $A$ and $B$ unkown?

 

[BvU]

That is called a straightforward calculation

 

[Stephen Tashi]

Does it make sense to have $x$ and $y$ be known and instead $A$ and $B$ unknown?

What would $a_1, a_2,b_1,b_2$ be? Known or unknown?

 

[kent davidge]

What would $a_1, a_2,b_1,b_2$ be? Known or unknown?

Sorry for not clarifying, I was regarding them as unkowns. Otherwise the solution would be obvious as @BvU pointed out.

I figured out the answer to my question. In such case, the system would be undetermined. It has either no solution of infinite solutions.

 

[mfb]

A and B have a unique value each that depends on all the parameters on the right side. They are never undetermined.