Sum of three numbers

Question

The sum of three numbers is 21. The sum of twice the first​ number, 4 times the second​ number, and 5 times the third number is 78. The difference between 7 times the first number and the second number is 43. Find the three numbers.

Answer 1

F+S+T = 21

2F+4S+5T = 78

7F-S = 43

You can solve with algebra, substitution & elimination, to get first number =7, second number = 6 and third = 8

or you can solve with matrix algebra

1 1 1 21

2 4 5 78

7 -1 0 43

reduce to

1 0 0 7

0 1 0 6

0 0 1 8

F=7, S=6, T= 8