Solve by substitution:

Question

y=x-4
x+y=14

Answer 1

Let's rewrite that as
y - x = -4
y + x = 14
Add those two equations to get
2y = 10
That tells you that y=5
Use either of the orginal equations to get x.

Answer 2

y=x-4
x+y=14

x+(x-4)=14
x+x-4=14
2x=18x
x=9

check answer
x+(x-4)=14
9+9-4=14
18-4=14
14=14

so 9 is your correct answer