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Solving Systems Of Equations And Inequalities: Elimination, Graphical, And Numerical Methods

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Solving Systems of Equations and Inequalities: Elimination, Graphical, and NumericalMethods1.Use the elimination method to solve the system of equations.8u+3v=-153u+v=-6We call the first equation (1) and the second one (2).We perform thefollowing calculation : (1)–3(2) : (8–3*3)u =-15 + 3*6 then–u = 3 then u =-3Hence v =-6–3u =-6 + 9 = 3The solution is then (u,v) = (-3,3)2. Solve the system of equations (a) symbolically, (b) graphically, and (c) numerically.(a) Here use the elimination method.What is the first step in the elimination method5x+y=7x-y=5We call the first equation (1) and the second one (2).The first step of the elimination method is to add the two equations to eliminate y : (1) + (2)then 6x = 12 then x = 2Hence y = x–5 = 2–5 =-3We’ve solved symbolically and numerically the system.As far as the graphically resolution, we plot the two lines (5x + y = 7 and x-y = 5) and theintersection will be the solution (the green curve is x-y = 5 and the red curve is 5x + y = 7)

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