Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. x' = 6x - 10y + sint y' = 5x - 4y - cost Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. O A. y(t) = Cert+C,te -t+ 162 138 629 - cost + - 629 sint B. y(t) = C, et cos 5t + C, et sin 5t+ 162 138 629 cost + - 629 sin t O c. y(t) = C, et + C,tet+ 162 138 629 cost + 629 sin t O D. y(t) = C1 e -t cos 5t + C2 e -t sin 5t+ 162 138 629 cost + 629 sin t O E. The system is degenerate. Now find x(t) so that x(t) and the solution for y(t) found in the previous step are a general solution to the system of differential equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. X(t) = O B. The system is degenerate.Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x' + y' - 3x - by = e -t x' + y' + 7x+ 2y = et Eliminate y and solve the remaining differential equation for x. Choose the correct answer below. O A. x(t) = C, e ot cos (6t) + C2 e ot sin (6t) + 5 e t 37 37 5 B. x(t) = C, cos (6t) + C2 sin (6t) + e 37 37 O c. x(t) = C1 e 6t + C, e - 6t + 5 -t . 37 37 O D. X(t) = C1 cos (6t) + C2 sin (6t) Now find y(t) so that y(t) and the solution for x(t) found in the previous step are a general solution to the system of differential equations. y(t) =