Your second equation is wrong.

Let x = the distance she runs
Ley y = the distance she walks

x + y = 6

That's the distance equation.

Now we must make a time equation.

We must use , not "distance times rate".

The time she runs = 

The time she walks = 

Now since she stops to rest 5 minutes, the total time
she walks and runs is only 55 minutes.  But we must change
55 minute to hours by dividing it by 60.  So the total
time is ths of an hour, which reduces to ths
of an hour.  So the second equation is



Then we clear that of fractions by multiplying
through by the LCD 




                   




So the system to solve is



Multiply the first equation through by -3
to eliminate the x's.  Add vertically term 
by term:

-3x - 3y = -18
 3x + 8y =  22
--------------
      5y = 4
       y = ths of a mile she runs.



Now multiply the first equation through by -8
to eliminate the y's.  Add vertically term by term:

-8x - 8y = -48
 3x + 8y =  22
--------------
-5x      = -26
  x      = 
       x =  = miles she walks. 

Edwin