Let's call "x" the larger number and "y" the smaller number.
The difference between the numbers is 5 : x - y = 5
The sum of the larger number and twice the smaller number is 14 :
x + 2y = 14
[tex] \left \{ {{x-y = 5} \atop {x+2y=14}} \right. [/tex]
[tex] \left \{ {{x=5+y} \atop {x+2y=14}} \right. [/tex]
Let's subsitute x in the second equation, it gives :
5 + y + 2 y = 14
5 + 3y = 14
3y = 14 - 5
y = 9/3 = 3
Let's substitute y in the first equation :
x - y = 5
x - 3 = 5
x = 5 + 3 = 8
Hope this helps !
Photon
