Final answer:
To solve the given system of differential equations by systematic elimination, multiply the first equation by 2 and the second equation by 7 to eliminate the y term. Then, subtract the second equation from the first equation to eliminate the y term. Finally, rearrange the equation to solve for y.
Step-by-step explanation:
To solve the given system of differential equations by systematic elimination, we can start by multiplying the first equation by 2 and the second equation by 7 to eliminate the y term. This gives us:
2(dx/dt) = 8x + 14y
7(dy/dt) = 7x - 14y
Next, we can subtract the second equation from the first equation to eliminate the y term:
2(dx/dt) - 7(dy/dt) = 8x + 14y - (7x - 14y)
2(dx/dt) - 7(dy/dt) = x + 21y
Finally, we can rearrange the equation to solve for y:
21(dy/dt) = 2(dx/dt) - x
dy/dt = (2/21)(dx/dt) - (1/21)x
So the solution to the system of differential equations is:
dx/dt = 4x + 7y
dy/dt = (2/21)(dx/dt) - (1/21)x