To solve this system of equations using elimination, we can eliminate one variable by adding the equations. Let's start by multiplying the second equation by 2 to make the coefficients of \(x\) the same:
Original equations:
\[2x + 2y = 4\]
\[2x + 6y = 12\]
Now, subtract the first equation from the modified second equation:
\[2x + 6y - (2x + 2y) = 12 - 4\]
\[4y = 8\]
Divide by 4:
\[y = 2\]
Now that we know the value of \(y\), substitute it back into the second equation to find \(x\):
\[x + 3(2) = 6\]
\[x + 6 = 6\]
\[x = 0\]
Therefore, the solution to the system of equations is \(x = 0\) and \(y = 2\).