There is no solution in whole numbers, because the problem is stated incorrectly.
"1.5 times older than..." means as old as, and then 1.5 more times as old as -- i.e., 2.5 times AS OLD AS. With that correct grammatical interpretation, the problem can't be solved.
The correct statement of the problem is this:
Patrick is 5 years older than his nephew. In 2 years he will be 1.5 times AS OLD AS his nephew. How old is each now?
With that statement of the problem, we have
(1) Patrick is 5 years older than his nephew
(2) Patrick's age in 2 years will be 1.5 times his nephew's age in 2 years
With the equations in this form, substitution seems appropriate:
