Is this computer able to be a gaming rig

Lenovo ThinkCentre 10A7000QUS Desktop Computer - Intel Core i7 i7-4770 3.40 GHz - Mini-tower - Business Black

Open your tower. Look at your Motherboard and power supply. If you have a PCI-E 2.0 or 3.0 expansion slot and at least 400 watt power supply then yes. Most likely you will have a PCI-E slot but the power supply will be cheap and low powered, but you can pick up a power supply suitable for pretty cheap.

thank you i was thinking of upgrading the power on it is higher then 400 watts bad for this rig can it be bad for a computer if thier is more the the voltage needed

Watts and Volts are two different things. More watts means you can power more/stronger components. Power supply voltage is pretty standard at 12 volts, and that cannot be changed. How many watts is your power supply rated for?

  • Input voltage: 120 - 230 VAC (50/60 Hz), RAID level: 0, 1

That is not the watts. It should say on the power supply what how many watts it is rated for and what certification it holds, 80 plus bronze, 80 plus gold, or 80 plus platinum. Example:

my power supply says 750 80 plus gold. So my power supply is rated for 750 watts.

285 watts max

yeah you will need to purchase a power supply. Any 500 watt power supply will be enough to power a graphics card, and you can usually pick one up for about $50 or $60, and it will last years.

An XFX 450W and a 7770 are affordable options that will enable you to game. How much are you looking to spend? The aforementioned components should cost £100/$100 in total. Not much at all.

I'd actually suggest a R9 250X or a 260X. The price difference is of negated by the additional performance. This going from a purely bang for the buck standpoint. Let-alone 7770s out in the wild are starting to dwindle. 

i really need something to withstand high amounts of gaming for many years that is affordable

Budget? Location?

less then 500 and nvidia model graphics card

less then 500 and nvidia model graphics card

For $500, you could do quite a lot with that. The XFX 550 is an affordable PSU that I always recommend.

Providing there is enough room in your case for these components, you can purchase a high-end Nvidia GPU with your remaining budget. Your system would run games really well.

This is your current build with $500 worth of upgrades... GTX 770, 550w modular Seasonic PSU, Corsair 200R case, and Kingston SSDNow 120GB SSD... away (you could try to fit it all into those awful Lenovo cases and get a better SSD I suppose... or get a bigger case and grab a non modular PSU... there's a lot of options... but that's what I'd do for $500...

thank you i learn so much from you guys thank you all and DRUNKENPANDA for all of your help