In　this　paper,　we　consider　and　solve　the　stabilizable　problem　of　second-order　linear　time-invariant　(LTI)　switched　systems　consisting　of　two　subsystems　with　unstable　foci.　Based　on　the　phase　plane　techniques,　firstly　we　single　out　the　＂most　stabilizing＂　state　trajectory　corresponding　a　special　switching　law.　The　switched　systems　would　be　stabilizable　if　the　＂most　stabilizing＂　state　trajectory　converges　and　vice　versa.　Then　analysis　results　reveal　that　the　switched　system　is　stabilizable　with　satisfying　a　set　of　inequalities.