Two numbers have a sum of 119 and a difference of 25. What are the two numbers? For writing and solving a system of equations?

Let x and y be the two numbers, where x > y.

x + y = 119 …… [1]
x - y = 25 …… [2]

[1] + [2] :
2x = 144
x = 72

Substitute x = 72 into [1] :
72 + y = 119
y = 47

Hence, the two numbers are 47 and 72.

You don't need to write lengthy equations to solve these types of questions,I will tell you a 'trick' to solve these questions in less than 15 seconds..
So.., to get the 2 numbers, just add the sum to the difference, that is, add 119 and 25,which is equal to 144,the larger of the 2 unknown numbers will be 144/2=72,the 2nd one will be 119-72=47.See, simple right!
Now, in case you bother to ask why this works, this is the mathematical explanation:
x+y=119
x-y=25
Adding both the equations,
x+y+x-y=119+25
x+x+y-y=144
2x=144
x=144/2=72
y=119-x=119-72=47

(Divide the 25 by 2: 25 / 2 = 12.5).....(Divide the 119 by 2: 119 / 2 = 59.5).....(Add the answer for both: 59.5 + 12.5 = 72).....(Subtract that from the original number: 119 - 72 = 47).....Those two numbers are your answer: 47 + 72 = 119.