3x – 2y = -11 and 5x + y =-1?'
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L = hours used by the Lopez's sprinkler
R = hours used by the Russell's sprinkler
so, we know the Lopez's sprinkler uses 15 Liters per hour, so say after 1 hour it has used 15(1), after 2 hours it has used 15(2), after 3 hours it has used 15(3) liters and after L hours it has used then 15(L) or 15L.
likewise, the Russell's sprinkler, after R hours it has used 40R, since it uses 40 Liters per hour.
we know that both sprinklers combined went on and on for 45 hours, therefore whatever L and R are, L + R = 45.
we also know that the output on those 45 hours was 1050 Liters, therefore, we know that 15L + 40R = 1050.
how long was the Lopez's on for? well, L = 45 - R.
R = hours used by the Russell's sprinkler
so, we know the Lopez's sprinkler uses 15 Liters per hour, so say after 1 hour it has used 15(1), after 2 hours it has used 15(2), after 3 hours it has used 15(3) liters and after L hours it has used then 15(L) or 15L.
likewise, the Russell's sprinkler, after R hours it has used 40R, since it uses 40 Liters per hour.
we know that both sprinklers combined went on and on for 45 hours, therefore whatever L and R are, L + R = 45.
we also know that the output on those 45 hours was 1050 Liters, therefore, we know that 15L + 40R = 1050.
how long was the Lopez's on for? well, L = 45 - R.
All the components in the state vector need to sum to 1. You're given that component corresponding to state 1 is 0.2, and that the component for state 3 is 0.
That leaves states 2 and 4, for which you're told that the component for state 2 is four times as large. If
is the component for state 
, then you have
which means
. So the state vector is 
.
That leaves states 2 and 4, for which you're told that the component for state 2 is four times as large. If
which means