The method of Example 2 can be used for linear systems with infinitely many solutions. Use that method to solve the systems in both parts at the same time.
(a) x1 - 2x2 + x3 = - 2
2x1 - 5x2 + x3 = 1
3x1 - 7x2 + 2x3 = - 1
(b) x1 - 2x2 + x3 = 1
2x1 - 5x2 + x3 = - 1
3x1 - 7x2 + 2x3 = 0