Difference of numbers. the larger of two integers is 8 less than twice the smaller. when the smaller number is subtracted from the larger, the difference is 17. find the two numbers.

Let's call the numbers x (the bigger) and y (the smaller)

The larger of two integers is 8 less than twice the smaller. this means:

x=2z-8
When the smaller number is subtracted from the larger, the difference is 17.

This means: x-z=17.

i'll insert
2z-8

instead of x, since it's equal to it: 
2z-8-z=17

2z-z is just z:
z-8=17

so

z=25.
and x must be 25+17=42

let's check:The larger of two integers is 8 less than twice the smaller.
twice the smaller is 50, and yes, 42 is 8 smaller than 50, it's correct!

so the two numbers are 25 and 42