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

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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*