How to boot back into Linux after Windows 10 install

Preface

On this computer I had Windows 7 installed. I accidentally broke it, so I installed Linux Mint (since Linux is free and I didn't want to pay for Windows). Recently I was able to install Windows 10 on the partition that previously contained my broken Windows 7 (I looked at all the files and decided that I had them (or equivalent) stored in other places).

Problem

Now this is where my problem comes in. Once I installed Windows 10, it boots up fine... the only problem is that the installation seems to have broken (possibly overwritten) the GRUB2 bootloader, and now I can't boot into Linux.

I've looked at many Q&As here on Super User, but none of them worked.
(so please don't mark this as a duplicate unless I say it works in my situation! Thank you)

Possible Solution #1

There was one that got pretty close to solving my problem. It was having me use EasyBCD to add Linux to the bootloader, but I didn't know where the boot files are stored in a Linux system.
I don't know how others are, but I have three partitions, one for the filesystem (which this is where I suspected the boot files to be, but it didn't work), one for /home (I was going to select this one next, but I wanted to ask this question, before I messed anything up anymore...), and one for the swap (I know the boot files aren't in this partition).

Possible Solution #2

One was talking about installing Linux and then using some BCD software to add it to the bootloader, would this work in my situation? When Linux is already installed?

Final thoughts

For anyone who answers my question just know that I don't care if I have the GRUB2 bootloader or a Windows bootloader (or one that looks like a Windows bootloader). I just want to be able to boot into both Linux and Windows when I want (since I've found that there are big pros to both)

Solution 1:

 Regarding your Possible Solution #1

I discourage the use Of EasyBCD.To keep it sort - it messes with bootloaders in unpredictable ways and hard to remove completely once installed

Rod-Smith on EasyBCD {Taken from this answer}

First, the last I heard, EasyBCD was useless for managing a Windows/Linux dual-boot on an EFI-based computer, so I recommend you stop trying to use it.

Regarding Possible Solution #2

If you mean like this use windows bootloader to boot linux (this is one of my previous answers)

If this is what you mean then no, this method will not work because linux already installed.

Possible solutions #1

1.Create a live USB from the ISO of whichever Linux you have

2.Boot the live system

3.Chroot the installed system and reinstall bootloader

3A.Mount your partition

sudo mount /dev/sda2 /mnt  #Replace sda2 with root partition

If you have a separate /boot, /var or /usr partitions

sudo mount /dev/sdXW /mnt/boot

sudo mount /dev/sdXY /mnt/var

sudo mount /dev/sdXZ /mnt/usr

3B.Bind mount some necessary stuff

for i in /sys /proc /run /dev; do sudo mount --bind "$i" "/mnt$i"; done

3C.If Ubuntu is installed in EFI mode

sudo mount /dev/sdXY /mnt/boot/efi

3D.chroot into your Ubuntu install

sudo chroot /mnt

3E.reinstall grub

grub-install /dev/sdx

3F.Update grub : Regenerate grub files by running update-grub

update-grub

3G.If everything worked without errors, then you're all set

exit
sudo reboot

Upon reboot Grub will help you boot desired OS

Solution 2:

The free Super Grub2 Disk should be able to fix the problem with one click: