Solving equation for sum of 2 variables

Question

Let's say I have a basic equation (here a linear combination): $$ax_1 + bx_2=y$$

Is there any way to get the value of the sum $x_1+x_2$ if $a$, $b$ and $y$ is known?

Answer 1

If there are no further restrictions on $x_1$ and $x_2$, then we cannot in general (see Lacklubs comment below) say anything about $x_1+x_2$, as the system is underdetermined, i.e., there are more variables than equations.

Answer 2

In the absence of any additional information, no.

For example, there are lots of pairs of numbers that differ by $1$, but their sum could be anything. Consider the pairs (0,1), (10,11), (1000, 1001).