I would like to solve this system of equation for X and Y : 
Do you know if their exist a mathematical solution to this system ? And how to solve it ? Or a numerical solution ?
If yes, do you think their is a way to solve it with Python ?
I would like to apply this solution to a gas sensing problem. My problem is that I measure 2 photoacoustic signal with 2 two different sensors. Each signal is a function of the concentration of CO2 and relative humidity. The equation for each signal is : 
C_gaz is a CO2 gas concentration in ppm. For the moment I'm measuring CO2 in a lab room. So it should be a positive real number between 0 and 5000 (usually around 400). X_RH is the realtive humidity in the room. It's a percentage. It's a real number between 0 and 100 (Not 0 and 1). It's very unlikely to be above 80 and under 20.
If I substract the signal to the first coefficient a_0, I end up with the system of equation I meantionned in the beginning.
The coefficients for the first sensor are :
- a0 = 2.210e-04
- a1 = 6.071e-07
- a2 = -1.942e-05
- a12 = 9.131e-08
- a11 = 1.258e-10
- a22 = 2.269e-07
and for the second sensor :
- a0 = -2.658e-04
- a1 = 4.486e-06
- a2 = 1.824e-05
- a12 = 4.013e-07
- a11 = 1.767e-11
- a22 = -2.623e-07
The PA signal I'm measuring is a real positive number. For the first sensor, It usually is between 1e-03 and 20e-3 V. You can consider it to be 2.4e-03 V. For the second sensor it usually is between 1e-03 and 20e-03 V. You can consider it to be around 13e-03 V .
I'm monitoring this signal for a couple hours. So I have a numpy array of a couple thousand elements containing the measured signal every 2 seconds approximately.
The data is here : https://www.dropbox.com/scl/fo/vzyk3r38shp3z1sccu6z5/AFeLzb-Rndw6deqmBrjtcBQ?rlkey=9xg0q357r12zk6io9h8gox6xs&st=ubah66bk&dl=0