First, we simplify the expressions:

2X + 3(X + Y) = 11
2X + 3X + 3Y = 11
5X + 3Y = 11

7(X + 3Y) - 4Y = -23
7X + 21Y - 4Y = -23
7X + 17Y = -23

Now we have a system of two equations:

1) 5X + 3Y = 11
2) 7X + 17Y = -23

We can solve this system of equations using the substitution method. From equation 1, we can express X in terms of Y:

5X = 11 - 3Y
X = (11 - 3Y) / 5

Now substitute this expression for X into equation 2:

7(11 - 3Y) / 5 + 17Y = -23
77 - 21Y + 85Y = -115
64Y = -192
Y = -192 / 64
Y = -3

Now substitute the value of Y back into the expression for X:

X = (11 - 3(-3)) / 5
X = (11 + 9) / 5
X = 20 / 5
X = 4

Therefore, the solution to this system of equations is X = 4 and Y = -3.