hm.
The first thing that springs to mind is that you don't need the system call here, you only need the backticks, e.g.,

my $text = `cat $file`;
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Do you know about perldoc? It's a great tool. It documents every single function in perl; it's a real lifesaver. Type

perldoc -f system
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at a prompt and you'll get all the info you need about system, and how to get the output of a command.

Just a suggestion:
I'd probably do something like the following:

#!/usr/bin/perl -w
use strict;
my $file;
my @files = glob("bin/*.pl");

foreach $file (@files) {
    open(FILE, $file) || die "Couldn't open $file: $!\n";
    while(<FILE>) {
         chomp $_;
         print("$_\n");
    }
    close(FILE);
}
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Use perldoc -f to look up each of the glob, open, die, while, chomp, and close functions.