let f = forks
let s = spoons
let k = knives
f + 5k = 4s, one fork and 5 knives balance 4 spoons.
3k = 2f + 2s, 3 knives balance 2 forks and 2 spoons.
isolate the term for the spoons in both equations to get
4s = 5k + f
2s = 3k - 2f, multiply this equation by -2 to solve the system using elimination to get
-4s = -6k + 4f
0 = -k + 5f, or
k = 5f,
2k = 10f
substitute k value into one of the original equations;
3k = 2f + 2s
3(5f) = 2f + 2s
15f = 2f + 2s
13f = 2s, or 2s = 13f
2s + 2k = 13f + 10f = 23f ... this means it takes 23 forks to balance two spoons and 2 knives.