I went to a state school (i.e. public school in American terminology) in a poor area and studied hard and did well, got scholarships, went to Uni etc.
There are some problems with people not being able to afford to dedicate time to study - this can be solved by offering a maintenance allowance to all students, as I believe is done in some Nordic countries.
But the biggest issue I saw in my high school was people either giving up on education altogether, or having unrealistic expectations leading them to choose University degrees with poor job prospects.
Note, I include the trades in education as in fact they better than many University degrees when it comes to helping people improve their lot in life.