svm optimization problem
I think that this system of equation is incorrect. If you know that (3, -1), (3, 1) and (1, 0) are support vectors then you need to solve the next system:

3*w1 - 1*w2 - w0 = ±1
3*w1 + 1*w2 - w0 = ±1
1*w1 + 0*w2 - w0 = ±1


Support vectors on the same side of the separation line have the same sign on the right side of the equation (same sign here: ±1). In this example, (1, 0) locates on one side, while (3, -1) and (3, 1) are on the other side. Thus, the system will be the following:

3*w1 - 1*w2 - w0 = 1
3*w1 + 1*w2 - w0 = 1
1*w1 + 0*w2 - w0 = -1


The solution is: w0 = 2, w1 = 1, w2 = 0. You can plot all the points and check that this solution is correct.