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
