Question

Combined, there are 178.
​Asians, Africans,​ Europeans, and Americans in a village.
The number of Asians exceeds the number of Africans and Europeans by 69.
The difference between the number of Europeans and Americans is 7.
If the number of Africans is​ doubled,
their population exceeds the number of Europeans and Americans by 23.
Determine the number of​ Asians, Africans,​ Europeans, and Americans in this village

Using a Matrix or matrices.

How many Asians:
Africans:
Europeans:
Americans:
In the village?

Answer 1

set this up with AS,AF,E,Am variables
As+0Af-E-Am=69
0As+0Af+E-Am=7
0As+2Af-E-Am=23
As+Af+E+Am=178

1,0,-1,-1,69
0,0,1,-1,7
0,2,-1,-1,23
1,1,1,1,178

row1+4>4
1,0,-1,-1,69
0,0,1,-1,7
0,2,-1,-1,23
2,0,0,0,247
something is wrong, we have a non-integer for number of Africans. Recheck the problem.