<s>[INST] To calibrate a thermometer, we need to find the \(C^{\circ}\) (Celsius degree) value for two fixed points: the freezing point of water (\(P_{1}\)) and the boiling point of water (\(P_{2}\)). When a thermometer is in contact with ice (freezing water), it reads \(x^{\circ}\), and it is known that \(P_{1}\) (\(0^{\circ}C\)) should correspond to \(x^{\circ}\). Similarly, the thermometer reads \(y^{\circ}\) when in contact with boiling water, and \(P_{2}\) (\(100^{\circ}C\)) should correspond to \(y^{\circ}\).[/INST]