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To solve this system using elimination, we will add the two equations together since the y-terms will cancel out:
4x - y + 7x + y = 23 + 21
11x = 44
x = 4
Now we can substitute this value back into one of the original equations to solve for y:
4(4) - y = 23
16 - y = 23
-y = 7
y = -7
Therefore, the solution of the system is (4, -7). So the correct response is:
(4, -7)