In elimination, we multiply one or both equations by cleverly chosen numbers, so that the two coefficients of the same variable in the two equations are opposite values. Then, we add the two equations, canceling that variable.
Here, we could leave the first equation as is, and multiply the second by (–2), so that the two x coefficients would be opposites.
Instead, to avoid negatives, I will simply multiply the first by 3 and leave the second as is, to cancel the y's.

3(4x + y = 5)= 12x + 3y = 15

12x + 3y = 15
2x – 3y = 13
14x = 28

x = 2, y = –3