Comparing (1) and (2), we notice that
a = d
And comparing (1) and (3), we also notice that
c = b + 5
Armed with this new info, let's play with (4). Substitute a with d and c with b + 5. We'd have:
b + 5 - a = 6
Subtract 5 from both sides to eliminate 5 from the left hand side. It becomes:
b - a = 1
-a + b = 1 .................. (5)
Recall
a + b = 8 .................. (1)
Now we see that (5) has the same variables as (1) so eliminate one variable. If you add both equations, you'd eliminate a, but if you subtract, b goes. Let's add.
-a + a + b + b = 1 + 8
0 + 2b = 9
b = 4.5
but a + b = 8
Therefore
a = 8 - b = 8 - 4.5 = 3.5
d = a = 3.5
Then
c - d = 6
c - 3.5 = 6
c = 6 + 3.5 = 9.5
