Book Maths Puzzle Algebra

I'm having trouble with solving systems. I did this before, at the beginning of the year, but I completely forget how to do it. Here's the system:
y=7x-9
y=4x+6

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Book Other Question
Solving the equation
Problem
4Y+7=5Y+13



But I need a breakdown, when I first tried to complete this problem I subtracted 7 from both sides but I was left with 9Y (4Y+5Y), I just need a break down I am doing someting wrong.



Thanks

Helpless in Durham Two consecutive integers are added together. The square of their sum is 361. What are the integers?