No starting values have been given, so we assume (0,0,0). However, these values cause the iterations to diverge.
The actual answer is (1,2,-1) for (I₁,I₂,I₃). The method is similar to Gauss-Seidel (already answered).
Rewrite the three linear equations making three other equations expressed in terms of each of the three unknowns.
I₁=(6I₂+I₃-9)/2; I₂=I₁-7I₃-6; I₃=4I₁-I₂-3.
See solution to Gauss-Seidel question as an example. The initial values should be provided so that divergence is avoided.
The difference between the two methods is that Seidel uses the latest updated variable values, while Jacobi uses the previous iteration’s values. Neither method seems to be effective for these two problems.