To solve these equations for a, we will isolate the variable a in each equation:

1) 18/a + 23 = 3/5

First, subtract 23 from both sides:

18/a = 3/5 - 23
18/a = 3/5 - 23/1
18/a = 3/5 - 115/5
18/a = -112/5

Next, multiply both sides by a to get rid of the fraction:

18 = -112a/5

Now multiply both sides by 5 to isolate the varaible a:

90 = -112a

Finally, divide both sides by -112:

a = 90 / -112
a = -0.80357 (rounded to 5 decimal places)

2) 4/7 = 8 + 2a/21

First, subtract 8 from both sides and multiply by 21:

4/7 - 8 = 2a
(4/7) 21 - 8 21 = 2a
12 - 168 = 2a
-156 = 2a

Next, divide by 2:

a = -156 / 2
a = -78

Therefore, the solution to the system of equations is a = -0.80357 and a = -78.