Try removing the memory module in the slot nearest the bottom case. This memory slot has a high rate of failure due to cracked solder joints. Usually if you press on the center of the bottom case while the laptop is powered on (and memory is in that slot) it will cause the laptop to freeze or get graphical glitches on the screen.
If you don't encounter any issues when pressing on the center of the Bottom Case, then try removing just a single module to see how it works. If you still have a problem, try swapping RAM so that you try each RAM stick by itself in each memory slot in order to determine which memory module or which memory slot is at fault.
I personally like to press directly on the wide plastic base of the memory slot (do not press on the memory module) to see whether that one memory slot has bad solder joints (memory must be installed in the slot nearest the bottom case for this test).
You can also lightly press on the memory module itself....if it causes a problem, then the module is not fully seated. Keep in mind when installing the second module, that the first installed module can become unlatched since they share the same flexing plastic arm for latching the memory. The little triangular protrusions can also become worn from installing/removing memory.
The good news is that it is extremely rare for two memory modules to fail at the same time, so you have everything you need for testing. It is possible both RAM slots can be bad though which would mean it is time to retire the laptop.
If the beeping stops, you may want to run a memory test for a bit of added assurance. You can use a bootable Memtest86 USB stick to test the memory. If you can consistently (or fairly consistently) find a failure with a certain RAM module or memory slot, then that makes things easier. If the default Memtest86 settings don't detect any issues, then try modifying Memtest86's CPU settings to "Sequential" or "Round Robin" since I have seen this sometimes help detect a problem, but just make sure only one physical memory configuration triggers a failure (or system freeze) with Memtest86 so you know it is not a bug with the test.
You can sometimes ignore any failure notices regarding test #13 the Hammer Test....one type of failure of the Hammer test may indicate bad RAM while another type of error for the Hammer Test is Ok to let pass.
I really would not recommend purchasing any more memory for this laptop especially since I have seen the memory slot nearest the bottom case have so many failures these Macs (I support thousands of Macs for my organization).