Consider a set of 2 tanks of water with 800 gal and 500 gal in each originally; liquid enters the firsttank at a rate of 15 gal/hour and exits the second tank at 15 gal/hour. Liquid flows out of tank 1 into1.tank 2 at 20 gal/hour and back into tank 1 from tank 2 at 5 gal/hour. If the liquid entering tank 1 has6 lb of sludge per gallon of water and each of the tanks has pure water in them to begin with, find asystem of equations that models your system. (Write in matrix form but do NOT solve...)

To write a system of equations that models the given system.Let x(t) be the amount of sludge in tank 1 and y(t) be the amount of sludge in tank 2 at any time t. Since both the tanks initially contain pure therefore x(t)=y(t)=0. The concentration of sludge is given by, Concentration of sludge=Amount of sludgeVolume in tank So, the concentration of sludge in tank 1 and tank 2 is given by, Concentration in tank 1=x800Concentration in tank 2=y500The rate of sludge is given by, Rate of sludge=Flow rate of waterConcentration So, the rate of change of the amount of sludge in tank 1 and tank 2 is given by, dxdt=Rate at which sludge enters the tank 1−Rate at which sludge leaves the tank 1dxdt=15 gal/hour6 lb/gal+5 gal/houry500−20 gal/hourx800dxdt=90+y100−x40 dydt=Rate at which sludge enters the tank 2−Rate at which sludge leaves the tank 2dydt=20 gal/hourx800−5 gal/houry500+15 gal/houry500dydt=x40−y100+3y100dydt=x40−y25 In matrix notation, we get x'ty't=−x40+y100x40−y25+900x'ty't=−1401100140−125xy+900 and the initial condition is x0y0=00x'ty't=−1401100140−125xy+900, x0y0=00