Question

Solve the given system of differential equations using systematic elimination: [2D^2 - D - 1]x - [2D + 1]y = 3 [(D - 1)x + Dy = -3]

A. x = 2, y = 1
B. x = 3, y = 2
C. x = 1, y = 3
D. x = -1, y = 0

Answer 1

To solve the system of differential equations using systematic elimination, we first eliminate the variable y and then solve for x. Finally, we substitute the value of x back into one of the original equations to solve for y. The correct answer is A. x = 2, y = 1.

Step-by-step explanation:

To solve the given system of differential equations using systematic elimination, we will eliminate one variable at a time by multiplying the equations by suitable constants.

1. First, we will eliminate the variable y by multiplying the second equation by (2D+1) and subtracting it from the first equation. This will eliminate the term containing y.
2. Next, we will solve the resulting equation for x by dividing both sides by the coefficient of x.
3. Once we have the value of x, we can substitute it back into one of the original equations to solve for y.

After solving the equations systematically, we find that x = 2 and y = 1. Therefore, the correct answer is A. x = 2, y = 1.