Those numbers are x=55 and y= 15.
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1) Gathering the data
x-y=40
4y=x+5
2) Rewriting the system, and then solving it
x-y=40 ⇒x=40+y
4y=x+5
Applying substitution in the 2nd equation
4y=(40+y)+5
4y =40+y+5 Subtracting y from both sides
4y-y= 40+y-y +5
3y=40+5
3y= 45 Dividing by 3
y=15
Replacing in the first equation
x-15=40 Adding 15 to both sides
x-15+15=40+15
x=55
3) Those numbers are x=55 and y= 15.