Use matrices to solve the system of equations (if possible.)

Question

4x + 9y + z = -17

{ 6x - 6y - 8z = 12

9x + 8y + z = -43

Answer 1

4x + 9y + z = -17

6x - 6y - 8z = 12

9x + 8y + z = -43

The 3x4 matrix to solve is 4 9 1 -17 using RREF, Reduced Row Echelon Form,

6 -6 -8 12

9 8 1 -43

yields:

x= -5

y= 1

z= -6

Answer 2

4 9 1 | -17

6 -6 -8 | 12

9 8 1 | -43

8*row 1 + row 2; -1*row1 + row3

----------------------------------------

4 9 1 | -17

38 66 0 | -124

5 -1 0 | -26

66*row 3 + row2

----------------------------------------

4 9 1 | -17

368 0 0 | -1840

5 -1 0 | -26

Equation #2 says 368 x = -1840 ---> x = -1840/368 = -5

equation #3 says 5x - y = -26

5(-5) - y =-26

-25 - y = -26

-y = -1

y = 1

original 2nd equation says 6x - 6y - 8z = 12

3x - 3y - 4z = 6

3(-5) - 3(1) - 4z = 6

-15 - 3 - 4z = 6

-18 - 4z = 6

-4z = 24

z = -6

x=-5 y = 1 z = -6

4 9 1 | -17 ---> 4(-5) + 9(1) + 1(-6) = -20 + 9 + -6 = -11 + -6 = -17 <-- YES!!!

6 -6 -8 | 12 ---> 6(-5) + -6(1) + -8(-6) = -30 + -6 + 48 = -36 + 48 = 12 <--- YES !!!

9 8 1 | -43 ---> 9(-5) + 8(1) + -6 = -45 + 8 + -6 = -51 + 8 = -43 <--- YES !!!

x=-5 y = 1 z = -6