$5\mathrm{.}9$: A sequential circuit has two J K flip$-$flops A and B and one input x$.$The circuit is described by the following flip$-$flop input equations:

JA$=$xKA$=$B

JB$=$xKB$=$A$\text{'}$

$($a$)$Derive the state equations A$($t$+1)$and B$($t$+1)$by substituting the input equations for the J and K variables.

$($b$)$Draw the state diagram of the circuit.

Also, $$the answer to part a$)$is supposed to be:

A$($t$+1)=$xB$\text{'}+$xA$\text{'}$B

B$($t$+1)=$xA $+$xA$\text{'}$B$\text{'}$

And I don't understand how or why? This answer was given to me in the back of the book in the "check your answers" section. Please help!