elimination

Solving the system, we get (x,y) = (3,2).

Let's first take a look at the first equation. We want to put x in terms of y. 

So, solving the equation, we have

$x+y=10-x-y\\ x=5-y$

Now, subsituting this into the second equation, we get that

$5-y-y=\left(5-y-1\right)+y-1\\$

This simplifies to 

$5-2y=3$

Now, for this equation, we get that y is equal to 1. 

Thus, subsituting this value into x, we find that

$x=5-1=4$

Thus, the answers for the equation are

$x=4,\:y=1$

So our final answer is $(4, 1)$

Thanks! :)