It is known that the system of equations x-2y = 1, x + 2Y = n and X + y = m, 2n-3y = 5 about XY have common solutions

It is known that the system of equations x-2y = 1, x + 2Y = n and X + y = m, 2n-3y = 5 about XY have common solutions

First solution x-2y = 1 (1)
2x-3y=5 (2)
(1)*2-(2)
-y=-3
y=3,x=1+2y=7
Substituting into the other two equations
n=x+2y=13
m=x+y=10