To solve this system, I would use substitution.
Since our first equation tells us that y = 2x - 3, we can substitute a
2x - 3 in for the y in our second equation to get 2x - 3 - 9 = -x.
Simplifying on the left we get 2x - 12 = -x.
Moving the 2x to the right, we have -12 = -3x.
Now divide both sides by -3 and we have 4 = x.
To find y, plug 4 back into either one of the original equations.
I'll go with the first one.
So we have y = 2(4) - 3.
Solving from here, we find that y = 5.
So the solution to this system is (4,5).