Question

Solve the system by Substitution.
-x-y-z=-8
-4x+4y+5z=7
2x+2z=4

Answer 1

- x - y - z = - 8                                 eq-1

- 4 x - 4 y + 5 z = 7                         eq-2

2 x + 2 z = 4                                    eq-3

consider equation 3

2 x + 2 z = 4

dividing each term both side by 2

(2x/2) + (2z/2) = 4/2

x + z = 2

z = 2 - x                                                  eq-4

consider eq-2

- 4 x - 4 y + 5 z = 7

using eq -4

- 4 x - 4 y + 5 (2 - x) = 7

- 4 x - 4 y + 10 - 5 x = 7

- 9 x  - 4 y = - 3

y = (3 - 9 x)/4                                                   eq-5

consider eq-1

- x - y - z = - 8

using eq-5  and eq-4

- x - ( (3 - 9 x)/4 ) - (2 - x) = - 8

multiplying each terms by 4

- 4 x - (3 - 9 x) - 4  (2 - x) = - 8

- 4 x - 3 + 9 x - 8 + 4 x = - 8

9 x - 11 = - 8

9 x = 3

x = 3/9

x = 1/3

using eq-4

z = 2 - x  

z = 2 - (1/3)  

z = 5/3

using eq-5

y = (3 - 9 (1/3))/4

y = (3 - 3)/4

y = 0