To solve the system of equations, we can use the method of elimination by multiplying the first equation by 4 to eliminate y:
4(3x+y) = 4(2)
12x + 4y = 8
Now we have the system of equations:
12x + 4y = 8
7x - 4y = 30
Adding the two equations together, we get:
(12x + 4y) + (7x - 4y) = 8 + 30
19x = 38
x = 2
Substituting x = 2 into the first equation, we get:
3(2) + y = 2
6 + y = 2
y = -4
Therefore, the solution to the system of equations is (2, -4).