(5) (Harder question) This question considers one application of systems of linear equations. The system should be solved using Gaussian elimination. The fuel consumption of a car depends on the road conditions it encounters. For example, on freeways, cars tend to drive faster, which can lead to higher fuel consumption. Conversely, in urban areas like Geelong, frequent stops also result in increased fuel usage. To assess the environmental impact, a researcher from Deakin University aims to quantify the fuel consumption on different road types. To this end, they have enlisted three individuals to monitor their fuel usage during their commutes in identical cars. • Mr. Tom Jerry first covers 19 kilometres through rural areas, then 23 kilometres on the freeway, and finally 4 kilometres in the city. • Ms. Ursula starts with 14 kilometres in rural areas, followed by 27 kilometres on the freeway, and concludes with 9 kilometres in Geelong. • Mr. Mickey Mouse's route consists of 15 kilometres through Geelong, followed by 7 kilometres on the freeway, and 16 kilometres through rural areas. Mr. Tom Jerry consumes 5 litres of fuel for his journey, Ms. Ursula uses 7 litres, and Mr. Mickey Mouse needs 9 litres. Let $x$ represent the fuel consumption in litres per kilometre in rural areas, $y$ for freeway travel, and $z$ for driving in Geelong. How many litres of fuel are needed per kilometre on the different types of road? Answer the question exactly.
