Both of those cards are unfortunately the last cards from AMD and Intel to not support Vulkan. Both the 7000 series (2012) and Broadwell (2015) support Vulkan.

I understand the frustration, but those are very old and very slow devices. A discrete GPU or a used laptop that supports Vulkan is likely less than $100-200 on eBay.

Worst case scenario, you could use llvmpipe software rendering on Linux, but it would be very slow.