So you know that:
2x+y=14+y
and
5x-y=x+13y
Here you have two equations with two unknown variables:
If you isolate x from the second equations you get:
x=(7/2)y
Insert that in the first equations and solve for y:
2*(7/2)y+y=14+y
y=2
Insert that value for y in one of the two equations (i chose the first):
2x+2=14+2
x=7
Therefore x=7
Hope that helped.
Actually you could start with isolating x, and then insert that in one of the two equations.