In 25–28, use the elimination method to find a general solution for the given system of three equations in the three unknown functions x (t), y(t), z(t).

Solution : Step 1 of 5 : In this problem, we need to use the elimination method to find a general solution for the given system of three equations in the three unknown functions x (t), y(t), z(t).Step 2 of 5 : Given three equations are x’ = x - 2y - zy’ = x + z z’ = 4x - 4y + 5zRewrite this equations in D form(D-1) x - 2y + z = 0 . . . . . . . (1)x - Dy + z = 0 . . . . . . . (2)4x - 4y + (5-D) z = 0 . . . . . . . (3)Step 3 of 5 : Solve this equations by elimination methodFirst eliminate one variable equation (2) * (5-D) - equation (3)(5-D-4) x + (4-(5-D)D)y = 0 . . . . . . . (4)equation (1) - equation (2)(D-2) x + (D-2) y = 0 . . . . . . . (5)