The sum of three numbers is 24. Twice the smallest number is 2 less than the largest number, and the largest number is equal to the sum of the other two.

Question

just need three equations so i can create the matrices and i can solve from there. 

Answer 1

x+y+z=24

(that is the sentence "the sum of three numbers is 24)

 

2z=x-2

(that is the sentence "twice the smallest number (2z) is (=) 2 less than the largest number (x-2)"

 

x=y+z

(that is the sentence "the largest number is equal to the sum of the other two")

 

This assumes that x is the largest and z is the smallest.  

Will want to put all of the variables on one side in a consistent order to set up your matrix.

 

 

Answer 2

Let the 3 numbers be x and y and z. x + y + z = 24; 2x = z - 2; z = x + y. Change equations to:

(1) x + y + z = 24;(2) 2x - z = -2;(3) x + y - z = 0. Add equation 1 to equation 3: (4) 2x + 2y = 24. Add equation  1 to equation 2: (5) 3x + y = 22. Multiply equation 4 by 3: (6) 6x + 6y = 72. Multiply equation 5 by 2: (7) 6x+2y = 44.

Subtract equation 7 from equation 6: 4y = 28, then y = 7. Substitute y=7 to equation 6: 6x + 6(7) = 72, 6x + 42 = 72,

6x = 30, x = 5. Substitute x=5 and y=7 into equation 1: 5 + 7 + z = 24; 12 + z = 24; z = 12.

check: 5 + 7 + 12 = 24; 2(5)= 12-2 = 10; 12 = 7 + 5.