or would I be violating the EULA?
It wouldn't hurt to read the EULA. Even a bit of it. Your answer starts on page 1, it finishes on page 2:
2. INSTALLATION AND USE RIGHTS.
a. One Copy per Computer. You may install one copy of the software on one computer. That computer is the “licensed computer.”
b. Licensed Computer. You may use the software on up to two processors on the licensed computer at one time. Unless otherwise provided in these license terms, you may not use the software on any other computer.
c. Number of Users. Unless otherwise provided in these license terms, only one user may use the software at a time.
d. Alternative Versions. The software may include more than one version, such as 32-bit and 64-bit. You may install and use only one version at one time.