Can I use both in the same computer?

Your system is only compatible with DDR4 memory. The layout of the pins on a DDR3 modules are completely different to that of a DDR4 module. You would be unable to install the DDR3 modules into your motherboard, if you attempted to do so, you would damage the module and/or the motherboard itself.

 

DDR4 SO-DIMMs have 260 pins instead of the 204 pins of DDR3 SO-DIMMs, spaced at 0.5 rather than 0.6 mm, and are 2.0 mm wider (69.6 versus 67.6 mm), but remain the same 30 mm in height.

Source: DDR4 SDRAM

Can I use both in the same computer?

Your system is only compatible with DDR4 memory. The layout of the pins on a DDR3 modules are completely different to that of a DDR4 module. You would be unable to install the DDR3 modules into your motherboard, if you attempted to do so, you would damage the module and/or the motherboard itself.

DDR4 SO-DIMMs have 260 pins instead of the 204 pins of DDR3 SO-DIMMs, spaced at 0.5 rather than 0.6 mm, and are 2.0 mm wider (69.6 versus 67.6 mm), but remain the same 30 mm in height.

Source: DDR4 SDRAM