how to solve system of 3 equations

Question

The Olympics have been held a total of 21 times in North America, Europe and Asia. The number of North Americans sites is 5 more than the total number of sites in Europe and Asia. There are four more sites in Europe than Asia. Find the number of Olympics sites each continent has held.

Answer 1

x+y+z = 21

x = y+z+5

x + x +5 = 21

2x = 16

x = 8 for North America

y+z = 21 -8 = 13

y=6 = Europe

z = 2 = Asia

Answer 2

Let's set up some equations for the no. of sites.:

N = No. America; E = Europe; A = Asia

N + E + A = 21

N = (E + A) + 5

E = A + 4. Replace E in the 2nd eqn:

N = A + 4 + A + 5 → N = 2A + 9

Now we have both N and E in terms of A. Substitute in 1st eqn:

(2A + 9) + (A + 4) + A = 21

4A + 13 = 21 → 4A = 8 → A = 2

Then E = 6 and N = 6 + 2 + 5 = 13

Check: N + E + A = 13 + 6 + 2 = 21