The fixed point algorithm should be the same as the one for single equation but the iteration function function will be a 2*1.

w1=y1+h*f(t,y1,y2)

w2=y2+h*g(t,y1,y2)

w=[w1;w2]

the iteration equation then

while y-y_1<tol

y=w

end

the solutions are:

y1=y(1)

y2=y(2)

hope that helps!