Solve Equations x+y+z=3,2x-y-z=3,x-y+z=9 using Elimination method

Solution:
Total Equations are `3`

`x+y+z=3 -> (1)`

`2x-y-z=3 -> (2)`

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

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Select the equations `(1)` and `(2)`, and eliminate the variable `y`.

`x+y+z=3`	` xx 1->`		``	`x`	`+`	`y`	`+`	`z`	`=`	`3`	``
		+
`2x-y-z=3`	` xx 1->`		``	`2x`	`-`	`y`	`-`	`z`	`=`	`3`	``
			``	`3x`					`=`	`6`	` -> (4)`

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Select the equations `(1)` and `(3)`, and eliminate the variable `y`.

`x+y+z=3`	` xx 1->`		``	`x`	`+`	`y`	`+`	`z`	`=`	`3`	``
		+
`x-y+z=9`	` xx 1->`		``	`x`	`-`	`y`	`+`	`z`	`=`	`9`	``
			``	`2x`			`+`	`2z`	`=`	`12`	` -> (5)`

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Now use back substitution method
From (4)
`3x=6`

`=>x=(6)/(3)=2`

From (5)
`2x+2z=12`

`=>2(2)+2z=12`

`=>2z+4=12`

`=>2z=12-4=8`

`=>z=(8)/(2)=4`

From (1)
`x+y+z=3`

`=>1(2)+1y+1(4)=3`

`=>1y+6=3`

`=>1y=3-6=-3`

Solution using Elimination method.
`x=2,y=-3,z=4`

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