Book Maths Puzzle Algebra

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

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Book Other Question

Agency pay 137 per day for equipment operators and 88 per day for general labor. if 39 people were hired and payroll was 4265 how many equipment operators were employed and how ma 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