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Solve this system of equations.   {2x+y+z=1 {-x-3y+z=9 {x-y+2z=7

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted February 28, 2013 at 2:24 AM via web

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Solve this system of equations.  

{2x+y+z=1

{-x-3y+z=9

{x-y+2z=7

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted February 28, 2013 at 4:00 AM (Answer #1)

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`2x+y+z=1` ---------(1)

`-x-3y+z=9` -------(2)

`x-y+2z=7 ` --------(3)

 

(1)+(2)

`2x+y+z-x-3y+z = 1+9`

`x-2y+2z = 10 ` -----(4)

 

(4)-(3)

`x-2y+2z-(x-y+2z) = 10-7`

`-y = 3`

`y = -3`

 

(2)-(1)

`-x-3y+z-(2x+y+z) = 9-1`

`-3x-4y = 8`

`-3x-4(-3) = 8`

`-3x+12 = 8`

`x = 4/3`

 

From (1)

`2x+y+z=1 `

`z = 1-2xx(4/3)-(-3)`

`z = 4/3`

 

So the answers are;

x = 4/3

y = -3

z = 4/3

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