A silly mistake (Quant)

From vaibhav.iit2002 on his BTG thread: 51 in QA - debrief.

"In DS, problems always think TWICE before marking C or E. Its a common GMAT problem to give an impression that you need both A and B to solve the problem while you can solve just by using A or B[both integers].
e.g. 2a + 3b = 10
21a + 23b = 67[i don't exactly remember the example]
Its very very easy to mark C as we think that we need 2 equations for 2 unknown variables. Try putting values for a and b[if feasible] in equation 2 as only a=1 and b=2 will fit."