By "linear combination" I'm assuming you mean the elimination method, which is fairly simple.
We can add, or subtract, one equation from the other to single out a specific value.
In this case, we can subtract the second equation from the first to isolate x.
(5x + y = 2) - (4x + y = 4)
Distribute a -1 to each term in the second equation.
-4x - y = -4
Add values vertically.
x = -2
Now that we have a value for x, we can solve for y.
4(-2) + y = 4
-8 + y = 4
Add 8 to both sides.
y = 12
The value of y is equal to 12.
