The solution of {x + y = m + 2; 4x + 5Y = 6m + 3} is an integer

The solution of {x + y = m + 2; 4x + 5Y = 6m + 3} is an integer

y=m+2-x
So 4x + 5m + 10-5x = 6m + 3
x=-m+7
If x is an integer, then M is an integer
Here y = m + 2-x is an integer
So m is any integer