5x + y = 2

4x + y = 4

use the linear combination method to solve

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.