Solve by the Newton–Raphson method the simultaneous, nonlinear equations

for x₁ and x₂ to within ± 0.001. As initial guesses, assume:
(a) x₁ = 2, x₂ = 5; 

(b) x₁ = 4, x₂ = 5; 

(c) x₁ = 1, x₂ = 1; 

(d) x₁ = 8, x₂ = 1.

x + x = 17 (8x) /3 + x/2 = 4