To solve for \(y\) in the system of equations \(y = x + 2\) and \(y = 3x - 4\), set the expressions for \(y\) equal to each other:
\[x + 2 = 3x - 4\]
Now, solve for \(x\). Subtract \(x\) from both sides and add 4 to both sides:
\[2 = 2x - 4\]
Add 4 to both sides:
\[6 = 2x\]
Divide by 2:
\[x = 3\]
Now that you have the value for \(x\), substitute it back into either equation to find \(y\). Let's use \(y = x + 2\):
\[y = 3 + 2 = 5\]
So, the solution to the system of equations is \(x = 3\) and \(y = 5\).