One number is eight less than the second number. Twice the first is 9 more than 3 times the second. Find the numbers

-49/3 and - 25/3

Step-by-step explanation:

Let the numbers be represented by f and s (first and second). Then f = s - 8. Also, 2f = 3s + 9. Solve this system for f and s:

Substituting s - 8 for f in the 2nd equation, above, yields

2 (s - 8) = 3s + 9, or 2s - 16 = 3s + 9. Then 3s = - 25, and s = - 25/3. The first number is then f = s - 8, or f = - 25/3 - 8, or f = - 49/3.