Solve the given system of differential equations by systemat

Solve the given system of differential equations by systematic elimination.

Solve the given system of differential equations by systematic elimination. 2dx/dt - 4x + dy/dt = e^t dx/dt - x + dy/dt = 5e^t

Subtracting second equation from first gives

x\'-3x=-4e^t

Integrating factor ie e^{-3t}

Multiplying by this integrating factor gives

(x\'-3x)e^{-3t}=-4e^{-2t}

(xe^{-3t})\'=-4e^{-2t}

Integrating gives

xe^{-3t}=2e^{-2t}+c1

x=2e^t+c1e^{3t}

x\'-x+y\'=5e^t

2e^t+3c1e^{3t}-2e^t-c1e^{3t}+y\'=5e^t

y\'=5e^t-2c1e^{3t}

INtegrating gives

y=5e^t-2/3 c1e^{3t}+c2