Systems of linear equations in three variables

Question

The sum of three numbers is 15. The sum of twice the first number, 5 times the second number, and 6 times the third number is 55. The difference between 7 times the first number and the second number is 53.

Find the three numbers.

Answer 1

x+y+z = 15

2x+5y+6z = 55

7x-y= 53

are 3 equations 3 unknowns

use substitution, elimination or matrix algebra

6x+6y+6z = 6(15)= 90

2x+5y+6z = 55

4x +y = 90-55= 35

7x-y =53

11x = 88

x =88/11 = 8 = the First Number

y=7x=53 = 56-53 = 3 = the Second Number

z = 15-8-3 = 4 = the Third Number

2(8)+5(3)+6(4) = 16+15+24= 55