Ran into a big problem because I neglected to export a database backup of my master site db. I have the backups of the site files for the master and each of the two slaves. And also the database backups of the two slaves.

I was planning to backup and then upgrade the sites from Joomla 3.7.5 to 3.8.0, and then to 3.8.2.

But I forgot and did the upgrade in one of the slave sites. Then I realized my error and logged into the Master and did the upgrade there.

Then I applied my patches and got a white screen in the admin area with this message:

"Error displaying the error page"

I ended up deleting the master files, and then re-extracting the 3.7.5 backup. I applied the patches and was able to log in to the master.

But when I got to the slave admin area, I get a white screen with this error message:

"Error displaying the error page"

I can I fix this?

If I understand correctly, you executed the Joomla Update from a slave site and not from the master website.
That would mean that you had the slave site DB upGraded and the PHP files and folders upGraded on the disk. In other words that the master files and folders correspond to J3.8.x and its DB for J3.7.5 that is inconsistent.

The error message "Error displaying the error page" correspond to something like an "Internal Server Error" in joomla.
Perhaps that you can get more info when enabling the joomla debug mode (see configuration.php file). When enabled, you will perhaps have additional info inside the /logs/xxxxx file.
The additional info will help identifying what cause this fatal error in joomla and collect the stack.
If you don't have the stack info then you will have to modify the source /librarires/src/Exception/ExceptionHandler.php to add the display of the stack to find the reason of the error and perhaps be able to fix it partially to give you the opportunity to complete the upGrade on the master.

UPDATE:

I was able to get the master upgraded to 3.8.2, and also the two slave sites. It's probably not the way you would have done it, but it mostly seems to be working.
The problem now is that I cannot apply the JMS patches. Doing so results in the following errors:

Error during installation of the file "libraries/cms/installer/installer.php"
Warning
Copy failed: /home/myaccount/domains/slave1.com/subdomains/parent/public_html/administrator/components/com_multisites/backup/libraries/cms/installer/installer.php to /home/myaccount/domains/slave1.com/subdomains/parent/public_html/libraries/cms/installer/installer.php
Copy failed: /home/myaccount/domains/slave1.com/subdomains/parent/public_html/administrator/components/com_multisites/backup/libraries/cms/installer/helper.php to /home/myaccount/domains/slave1.com/subdomains/parent/public_html/libraries/cms/installer/helper.php
Copy failed: /home/myaccount/domains/slave1.com/subdomains/parent/public_html/administrator/components/com_multisites/backup/libraries/joomla/user/user.php to /home/myaccount/domains/slave1.com/subdomains/parent/public_html/libraries/joomla/user/user.php
Copy failed: /home/myaccount/domains/slave1.com/subdomains/parent/public_html/administrator/components/com_multisites/backup/libraries/legacy/view/legacy.php to /home/myaccount/domains/slave1.com/subdomains/parent/public_html/libraries/legacy/view/legacy.php
Message
One or more backup file is missing. The original file(s) can not be restored.

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I tried uploading the files from my J3.7.5 backup which were in the libraries, but that didn't work. It gave me the white page with the "Error displaying the error page" message.

Btw, in the /libraries/cms/ in the 3.8.2 version there are only these directories: class, html, and less. But in the 3.7.5 version there are about 30 directories.

While finding out what to do to resolve the latest report might be helpful, I'm going to try to restore from an older backup first. And then do the upgrading the proper way. Hopefully the backup won't require too much redoing of things. I'll keep you posted.

Copy Fails means that you probably have a permission issue that forbid the copy.