X-y+4z=5
4x+z=2
x+5y+z=17

x = 0, y = 3, z = 2

Step-by-step explanation:

The given system of equations is expressed as

x - y + 4z = 5 - - - - - - - - - - - - - -1

4x + z = 2

z = 2 - 4x- - - - - - - - - - - - - -2

x + 5y + z = 17- - - - - - - - - - - - - -3

From equation

Substituting equation 2 into equation 1 and equation 3, it becomes

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

x - y + 8 - 16x = 5

x - 16x - y = 5 - 8

- 15x - y = - 3 - - - - - - - - - - - - - -4

x + 5y + 2 - 4x = 17

x - 4x + 5y = 17 - 2

- 3x + 5y = 15- - - - - - - - - - - - - -5

We would eliminate y by multiplying equation 4 by 5 and equation 5 by 1. It becomes

- 1

- 75x - 5y = - 15

- 3x + 5y = 15

Adding both equations, it becomes

- 78x = 0

x = 0

Substituting x = 0 into equation 2, it becomes

z = 2 - 4 × 0

z = 2

Substituting x = 0 and z = 2 into equation 1, it becomes

0 - y + 4 × 2 = 5

- y + 8 = 5

y = 8 - 5

y = 3

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