[Doubt] Conversion of finite automata to regular expression

Question

How to convert given finite state automaton into regular expression.

Comments

when you will remove q1, then loop 'xy' will be added on q0 as well as transition 'xy' will be added from q0->q2

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let we have removed q1 then what is the all transitions which may be lost....

1. q0->q1->q0     xy    (it could be represented as self loop on q0)

2.q0->q1->q2      xy    (it could be obtained by taking transition from qo->q2 as xy)

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I didn't knew how to handle this case. Thank you very much :)

Answer 1

"  (X+Y)*X (Y(X+Y)X)* (X+Y) (Y+Z)   "  i got this RE

Answer 2

(yz+(x+z))*(y+y+z)

Comments

Plz explain it with state elimination method