When I do the function using the hardware button it does not open "Android System Recovery" and did everything right.

WARNING! Applying a master reset on your smartphone will return its settings to factory values, and will result in deletion of personal data located on the phone's internal storage, including downloaded apps, contacts, downloaded content, custom ringtones and downloaded / captured images. NOTE: data stored on the SD or SIM cards are not going to be affected by a factory reset.

NOTE: Before proceeding with the master reset, you might want to learn how to back up your data and restore it on the Galaxy SIII Slim. Visit this link for a full back up guide, and this link for a full restore guide.

Master Resetting Through the Settings Menu:

1. While viewing the home screen, press the "Menu" button
2. Tap "Settings"
3. Access the "Accounts" tab
4. Tap "Backup and reset" under "Backup options"
5. If desired, clear the check boxes associated with "Automatic restore" and "Back up my data"
6. Tap "Factory data reset" > "Reset device"
7. Assuming that you have the screen lock enabled, you will be required to enter your password or PIN, and then tap "Continue"
8. Tap "Delete all" to confirm, and wait for your device to complete the process

Master Resetting Using Hardware Buttons:

NOTE: this method of applying a factory reset should be used only if the smartphone prevents you from resetting it via the settings menu; whether it crashes or freezes.

1. If possible, back up the data on your device (See the links above)
2. With the smartphone turned off, press and hold "Volume Up", "Home" and "Power" at the same time
3. After the phone vibrates, release the "Power" key and continue pressing the "Home" and "Volume up" buttons
4. Once the "Android System Recovery" screen appears, release all the hardware keys
5. From the recovery menu, press the "Volume down" button in order to navigate to, and highlight "wipe data / factory reset"
6. Press "Power" to select the option
7. Navigate to and highlight "delete all user data", using the "Volume down" button
8. Press "Power" to select the option, and wait for your smartphone to apply the factory reset
9. Once the process is complete, the "Reboot system now" option should be highlighted
10. Press the "Power" button to reboot your device in normal mode