Hibernation worked flawlessly on Windows 10 just before I've switched to Ubuntu (16.04), so I know for sure that the laptop (Lenovo y50) supports it.
Here's some info about the system:
$ sudo systemctl hibernate
Failed to hibernate system via logind: Sleep verb not supported
$ free -m
total used free shared buff/cache available
Mem: 15952 2953 11727 409 1271 12258
Swap: 16295 0 16295
$ cat /sys/power/state
freeze mem
$ ls /lib/modules/$(uname -r)/kernel/drivers/acpi
acpi_configfs.ko acpi_ipmi.ko apei ec_sys.ko sbshc.ko video.ko
acpi_extlog.ko acpi_pad.ko dptf nfit sbs.ko
Tried the instructions of the docs, editing the file with the right config:
/etc/polkit-1/localauthority/50-local.d/com.ubuntu.enable-hibernate.pkla
[Re-enable hibernate by default in upower]
Identity=unix-user:*
Action=org.freedesktop.upower.hibernate
ResultActive=yes
[Re-enable hibernate by default in logind]
Identity=unix-user:*
Action=org.freedesktop.login1.hibernate;org.freedesktop.login1.handle-hibernate-key;org.freedesktop.login1;org.freedesktop.login1.hibernate-multiple-sessions;org.freedesktop.login1.hibernate-ignore-inhibit
ResultActive=yes
Also tried other locations, which I've found in other places on the internet:
/var/lib/polkit-1/localauthority/10-vendor.d/com.ubuntu.desktop.pkla