\frac{dy}{dx} = f(x, y(x), z(x)), y(x_{0}) = y_{0}

\frac{dz}{dx} = g(x, y(x), z(x)), z(x_{0}) = z_{0}

k_{1} = hf(x_{n}, y_{n}, z_{n})

l_{1} = hg(x_{n}, y_{n}, z_{n})

k_{2} = hf(x_{n} + h/2, y_{n} + k_{1}/2, z_{n} + l_{1}/2)

l_{2} = hg(x_{n} + h/2, y_{n} + k_{1}/2, z_{n} + l_{1}/2)

k_{3} = hf(x_{n} + h/2, y_{n} + k_{2}/2, z_{n} + l_{2}/2)

l_{3} = hg(x_{n} + h/2, y_{n} + k_{2}/2, z_{n} + l_{2}/2)

k_{4} = hf(x_{n} + h, y_{n} + k_{3}, z_{n} + l_{3})

l_{4} = hg(x_{n} + h, y_{n} + k_{3}, z_{n} + l_{3})

k = \frac{1}{6}(k_{1} + 2k_{2} + 2k_{3} + k_{4})

l = \frac{1}{6}(l_{1} + 2l_{2} + 2l_{3} + l_{4})

x_{n+1} = x_{n} + h

y_{n+1} = y_{n} + k

z_{n+1} = z_{n} + l