Solve the system of equations using matrices. Use the Gaussian elimination method with back-substitution. x+y-z=-3
4x-y+z=8
-x+5y-4z=1

The solution set is ?

Step-by-step explanation:

Ⅰ.  x+y-z =-3

Ⅱ.  4x-y+z =8

Ⅲ.  -x+5y-4z =1

Use equation Ⅰ to eliminate the x terms from equations Ⅱ and Ⅲ.  

Ⅰ.  x+y-z =-3

Ⅱ.  -5y+5z =20

Ⅲ.  6y-5z =-2

Divide equation Ⅱ by the coefficient of its y term:  

Ⅰ.  x+y-z =-3

Ⅱ.  y-z =-4

Ⅲ.  6y-5z =-2

Use equation Ⅱ to eliminate the y terms from equation Ⅲ.  

Ⅰ.  x+y-z =-3

Ⅱ.  y-z =-4

Ⅲ.  z =22

Divide equation Ⅲ by the coefficient of its z term:  

Ⅰ.  x+y-z =-3

Ⅱ.  y-z =-4

Ⅲ.  z =22

Back-substitution  

y = -4 - (-1)z = 18

x = -3 - (1)y - (-1)z = 1

42.4

step-by-step explanation:

convert to decimal

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step-by-step explanation: