What upgrade do you recommend for an old system?

Hi everyone,
I have two old systems that I want to upgrade with the goal of making them play at 60 fps with high settings once again (if possible, my budget is really constrained right now due to the whole COVID thing)
The first system's specs are Core i5-4460, 12 GBs of RAM (2×4 GB & 2×2 GB), GTX 950 and a 750W PSU
and second's are Core i3-3240, a single stick of 8 GB RAM, GT 730 and 500W PSU (with a single 6-Pin Connector)

My budget is around 400 USD (converted from my currency) for both machines
 
Is that $400 for each system or $400 in total, to cover both computers? If it's the latter, then you're best off just replacing the graphics card in the first machine, and putting the GTX 950 into the second one. It's not enough money to replace the CPU, motherboard, and RAM in both machines.

$400 will get you a really good upgrade from that GTX 950 - e.g. a Radeon RX 5700 XT or a GeForce RTX 2060.
 
Is that $400 for each system or $400 in total, to cover both computers? If it's the latter, then you're best off just replacing the graphics card in the first machine, and putting the GTX 950 into the second one. It's not enough money to replace the CPU, motherboard, and RAM in both machines.

$400 will get you a really good upgrade from that GTX 950 - e.g. a Radeon RX 5700 XT or a GeForce RTX 2060.
sorry I didn't clarify, no unfortunately that's 400 all, (each system gets 200)
My idea was getting an RX 580 for each system and upgrading the small one's PSU (however this would streatch the budget by a bit that I didn't account for initially)
 
I keep forgetting just how cheap RX 580s are, and they’ll be a good upgrade for both machines. Unless the 500W PSU is a really cheap brand, it will be fine with the RX - the only issue is that it uses an 8 pin PCIe power connector. Your current PSU only has 1 six pin, but you could buy a molex-to-8 pin or 6-to-8 pin adapter rather than replacing the whole thing.
 
Is that $400 for each system or $400 in total, to cover both computers? If it's the latter, then you're best off just replacing the graphics card in the first machine, and putting the GTX 950 into the second one. It's not enough money to replace the CPU, motherboard, and RAM in both machines.

$400 will get you a really good upgrade from that GTX 950 - e.g. a Radeon RX 5700 XT or a GeForce RTX 2060.
sorry I didn't clarify, no unfortunately that's 400 all, (each system gets 200)
My idea was getting an RX 580 for each system and upgrading the small one's PSU (however this would streatch the budget by a bit that I didn't account for initially)
I keep forgetting just how cheap RX 580s are, and they’ll be a good upgrade for both machines. Unless the 500W PSU is a really cheap brand, it will be fine with the RX - the only issue is that it uses an 8 pin PCIe power connector. Your current PSU only has 1 six pin, but you could buy a molex-to-8 pin or 6-to-8 pin adapter rather than replacing the whole thing.
I admit the temptation to save that 70 dollars is real (Yeah I know prices are really high in my country) but at the same time I have had really really cheap chinese PSUs fail on me before so I know the risks (though luckily the systems all got out unscathed)
This current PSU isn't exactly terrible but it has quite a lot of cut corners
 
RAM, SSD, graphics card, and processor are the most frequently seen upgrades in various pc upgrade guides. But if want to get instant improvement on computer performance, RAM, SSDs, are very simple and necessary PC upgrades. If you are a gamer, graphics card is also important.
 
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