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May be a Dell model GX270 per this
Dell link.
There should be a service sticker either on the back of the case or on the bottom. It will have a model number and service number for reference. That is the best way to find out what the system was built as.
Some motherboards are used in many models.. others are more dedicated to specific models. That service tag will be your best resource.
With the smaller computer cases, only certain motherboard designs will fit. Same with the power supply. If a mid-tower or full-tower, the choices are much broader as to upgrades. But many products from Dell and HP are dedicated designs, and only specific replacements or upgrade parts are available.. some times only from that OEM source. Dell and HP (plus other brands) do not make their own motherboards.. just assembly of the systems. But when an OEM company places an order of several thousand motherboards, the parent manufacturer will gladly make production runs of different designs! They may be nearly identical to OEM setups, or much different.