Solve the system. Check your solution if possible.

-2x+y+4z = 5     (1)     

x+3y-z = 2          (2)

4x+y-6z = 11       (3)     

Multiplly (2) by - 4    and add it to (3)

-4x - 12y + 4z  = - 8

 4x +    y -  6z  = 11

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        -11y - 2z  = 3   (4)

Multiply (2) by 2 and add it to (1)

2x + 6y - 2z  = 4

-2x + y + 4z  = 5

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        7y + 2z  = 9    (5)

Add (4)  and (5)

-11y - 2z  = 3

 7y  + 2z  = 9

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-4y   = 12         divide both sides by -4

y = -3

And using (5)  ....     7(-3) + 2z  = 9   →  -21 + 2z = 9   → 2z = 30  → z = 15

And using (2)   ...... x+3(-3) - 15 = 2  →  x - 9 - 15  = 2 →  x = 26

So   { x, y, z }   = { 26, -3, 15 }