The Method of Elimination Example Find the particular solution of the system x=4x-3y,y'=6r-7y (3) that satisfies the initial conditions x(0)=2,y(0)=-1 Solution:If we solve the second equation in(3)for x,we get (4) so that (5) 4口0y4主，元，3000 Linear of Differential EquationsThe Method of Elimination Example Find the particular solution of the system x 0 = 4x−3y, y 0 = 6x−7y (3) that satisfies the initial conditions x(0) = 2, y(0) = −1. Solution: If we solve the second equation in (3) for x, we get x = 1 6 y 0 + 7 6 y, (4) so that x 0 = 1 6 y 00 + 7 6 y 0 . (5) Linear Systems of Differential Equations