We substitute it into R1:
EDIT: You made a typo the second time you wrote R1 and reversed a sign.
find a solution to the system:
5a1 + 2a2 - 3a3 = 4
a1 - a2 + 2a3 = -1
we can eliminate a1 from the second row by using R1 - 5R2 -> R2, which
5a1 - 2a2 - 3a3 = 4
7a2 - 13a3 = 9
from the second equation we obtain:
a2 = 1/7 (9+13a3)
We substitute this expression in the first equation and solve for a1 in
terms of a3. We find that
a1 = 2/7 - 1/7 a3
I can understand everything up to this point. However I cannot see how this has been substituted or how one can do this. Can anyone illustrate precisely what has happened in the last step?