2003 Cavalier

Have you tried a new bulb yet?

Check the headlight bulbs. Such bulbs have 2 different circuit in them and any one can fail with the other working.

Which means Hi and Low beamer 2 different circuit that shares the same common ground

I learned that this was the issue after I changed the bulb. The left light is out while on low beams but the right is on. And when I switch to hi beams the the left goes out and the right goes on. So I replaced the left bulb and the same result.

Should I replace both bulbs?

You mean after replacement of the left bulb, it still does not work on low beam?

Try swapping between right and left to see if there are any differences.

Ok i'll try that..switching left and right bulb

That didn't change anything
I checked both left and right headlight fuses..both ok
And other ideas?

High and low beam fuses operates both sides respectively and since at least one position is working, it is not the fault of the fuses.

You have a break in the wiring circuit between the right and left headlamps, one for the high beam and the other for the low beam.

Check the connectors for forward light harness, about 75 cm from horn connector. Wire color is Dark/Blue. It is for the low beam lights.

Use a fuses jumper to ground the Dark/Blue wire of leaft low to test if the low beam comes on for the left side. Grounding the Pink ( or Orange) wire would turn the high beams on.

Repeat above at right side headlamp.

The other connector for the high beam is at engine harness, left rear of engine.

Check for corrosion at connecter terminals. Corrosion of terminals would result in a break in the circuit.

A test lamp to test for voltage or a DVOM to test continuity would help.

Unplug both head light connectors and test for continuity between above described wires would enable you to understand if there is a break between them.