Question

Solve the system of equations using matrices. Use the Gaussian elimination method with​ back-substitution.

Answer 1

Answer:

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