Can you push a liquid and a gas into a container at different pressures? I have a gas ($\ce{CO2}$ for example) and I want to infuse it into a liquid ($\ce{H2O}$ for example). I need a higher pressure of $\ce{CO2}$ to do this. So I push in water into a sealed container (at 7 psi) and add $\ce{CO2}$ (at 14 psi).

Is this possible? Will it back up? What if I use a check valve? Can I use a non-electrical actuator of some sort to let liquid in, and then add gas 'automatically'? What about something that functions like a carburetor?

I need to let the new solution out after it is mixed and also allow a consistent flow if I leave the exit open. If I have a liquid at 7 psi and a gas at 14 psi and I am trying to push them both into a sealed container, how is this done? Letting it out? Doing it on the fly?

I know you do NOT carbonate water at these pressures. Just an example with real gas/liquid.
Pressure is due to the random impact of molecules on the surface, regardless of whether water or carbon dioxide or anything else. Once equilibrium is reached, all components are at the same pressure.

That said, there's no problem using a moving stream of $\ce{CO2}$ to propel and to mix with water at much lower pressure, using Bernoulli's principle. The automotive carburetor and spray atomizer operate on this basis.

The alternative, of course, is to add the water to the container through a check-valve, then add $\ce{CO2}$ at a higher pressure.

The choice is a continuous process vs. a batch process.