Starting with the two equations:
Y = x + 3 (1)
Y = 3x + 1 (2)
We can solve for x and y by equating equation (1) and (2) and solving for x.
x + 3 = 3x + 1
2x = 2
x = 1
Now we can substitute x = 1 into either equation (1) or (2) to solve for y.
Using equation (1):
Y = x + 3
Y = 1 + 3
Y = 4
Therefore, the solution for the system of equations is:
x = 1, y = 4