I need to upgrade my graphics card.?

I would like to upgrade my computer to use this graphics card. Would it work?

eVGA GeForce GTX 460 SuperClocked Graphics adapter - 1 GB - GDDR5 SDRAM

My Operating System information.

Operating System: Windows 7 Home Premium 64-bit (6.1, Build 7600) (7600.win7_gdr.110408-1633)

Language: English (Regional Setting: English)

System Manufacturer: HP-Pavilion
       System Model: NY639AA-ABA p6213w
               BIOS: BIOS Date: 07/24/09 10:38:20 Ver: 5.41
          Processor: Pentium(R) Dual-Core  CPU      E5300  @ 2.60GHz (2 CPUs), ~2.6GHz
             Memory: 6144MB RAM
Available OS Memory: 6134MB RAM
          Page File: 1720MB used, 10546MB available
        Windows Dir: C:\Windows
    DirectX Version: DirectX 11
DX Setup Parameters: Not found
   User DPI Setting: Using System DPI
 System DPI Setting: 96 DPI (100 percent)
    DWM DPI Scaling: Disabled
     DxDiag Version: 6.01.7600.16385 32bit Unicode

 Card name: Intel(R) G33/G31 Express Chipset Family
       Manufacturer: Intel Corporation
          Chip type: Intel(R) GMA 3100
           DAC type: Internal
 Display Memory: 256 MB
   Dedicated Memory: 0 MB
      Shared Memory: 256 MB
       Current Mode: 1920 x 1080 (32 bit) (60Hz)
       Monitor Name: HP 2159 Series Wide LCD Monitor
      Monitor Model: HP 2159
         Monitor Id: HWP282A
        Native Mode: 1920 x 1080(p) (60.000Hz)
        Output Type: HD15
        Driver Name: igdumd64.dll,igdumdx32
Driver File Version: 8.15.0010.1825 (English)
     Driver Version: 8.15.10.1825
        DDI Version: 9Ex
       Driver Model: WDDM 1.0
  Driver Attributes: Final Retail
   Driver Date/Size: 6/16/2009 04:32:08, 5471232 bytes
        WHQL Logo'd: Yes

You didn't need to post the specs, all we needed to know is that you have an HP Pavilion p6213w.

It's not absolutely necessary that your system has a PCIe x16 2.0 slot in order to use a 2.0 card. According to PCI-SIG, cards and motherboards that use the PCI Express interface are forward and backward compatible between the 1.x spec and the 2.x spec.

The GTX 460 will work in that system as long as you upgrade your power supply, your systems stock 250W psu (power supply unit) won't cut it.

Your systems specs-
http://h10025.www1.hp.com/ewfrf/wc/document?docname=c01869190&tmp_track_link=ot_faqs/top_issues/en_us/c01869190/loc:3&lc=en&dlc=en&cc=us&lang=en&product=4006023#N349

According to nvidia, in order to use the GTX 460 your system will need AT LEAST a 450W psu with two 6 pin pcie power connectors. (see Specifications tab)
http://www.nvidia.com/object/product-geforce-gtx-460-us.html

Most 450W psu's will only have one 6 pin connector, but most 500W or greater psu's will have at least two. That system uses an ATX power supply, very common and easy to replace. I'd recommend Antec, Corsair, Enermax, OCZ, Seasonic or Silverstone, all are decent brands.
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&N=100007657%20600014006&IsNodeId=1&bop=And&Order=RATING&PageSize=50
If you're in Canada-
http://www.newegg.ca/Store/SubCategory.aspx?SubCategory=58&name=Power-Supplies&Order=RATING

Just make sure that the power supply you get has all of the connectors that you'll need.
For example:
Your systems motherboard uses a 4 pin 12v ATX connector for the processor (a 4+4 pin or 8 pin will also work, you only use what you need) and a 24 pin main.
Graphics card needs 2x 6 pin pcie power connectors.
And whatever SATA or Molex connectors that you need for the drives (HDD and DVD).

Motherboard specs-
http://h10025.www1.hp.com/ewfrf/wc/document?docname=c01324212&lc=en&dlc=en&cc=us&product=4006023