Solve the following system of equations: 3x - 2y + z = 1, x + y + z = 4 and 2x + 2y - 3z = 8

Since the
equation was solved for `z` , replace all occurrences of `z`in the other
equations with the solution `(-3x+2y+1)` .


`z=-3x+2y+1 `
`x+y+(-3x+2y+1)=4 `
`2x+2y-3(-3x+2y+1)=8 `



Remove the parentheses around the
expression `-3x+2y+1` .

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

`x+y-3x+2y+1=4 `

`2x+2y-3(-3x+2y+1)=8`


Combine all
similar terms in the polynomial
`x+y-3x+2y+1` .

`z=-3x+2y+1`
`-2x+3y+1=4`

`2x+2y-3(-3x+2y+1)=8`


Multiply `-3`by
each term inside the parentheses.


`z=-3x+2y+1`
`-2x+3y+1=4`
`2x+2y+9x-6y-3=8`



Combine all similar
terms in the polynomial `2x+2y+9x-6y-3` .


`z=-3x+2y+1 `
`-2x+3y+1=4`
`11x-4y-3=8`



Move all terms not containing `x`to the
right-hand side of the equation.


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

`11x-4y-3=8`


Divide each
term in the equation by `-2` .


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

`x = (3y)/2 -
3/2`
 
`11x-4y-3=8 `


Since the
equation was solved for `x` , replace all occurrences of `x`in the other
equations with the solution `((3y)/2 - 3/2).`


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

`x = (3y)/2 - 3/2`

`11 ((3y)/2 - 3/2) - 4y - 3= 8`
 



Multiply `11`by each
term inside the parentheses.


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

`x = (3y)/2 - 3/2`

`(33y)/2 - (33)/2 - 4y - 3 = 8`
 



Combine `(33y)/2 - 4y` into a single
expression by finding the least common denominator
(LCD). The LCD of `(33y)/2 - 4y`  is `2` .


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

`x = (3y)/2 - 3/2`

`(25y)/2 - (33)/2 - 3 = 8`
 



Combine `-(33)/2 - 3`  into a single
expression by finding the least common denominator
(LCD). The LCD of `-(33)/2 - 3`  is `2` .


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

`x = (3y)/2 - 3/2`
 

`(25y)/2 - (39)/2 = 8`



Move all
terms not containing `y`to the right-hand side of the
equation.

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

`x = (3y)/2 -
3/2`
 

`(25y)/2 = (55)/2`




Multiply `55 * 2`  to get `110`in the
numerator.

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

`x = (3y)/2 -
3/2`

`25 y = (110)/2`


Reduce the
expression by canceling out all common factors from the
numerator and denominator.


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

`x = (3y)/2 - 3/2`  

`25y=55`


Since the equation
was solved for `y` , replace all occurrences of `y`in the other equations
with the solution `(11/5).`  

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

`x = (3y)/2 - 3/2`  

`y = 11/5`




Since the equation was solved for `y`
, replace all occurrences of `y`in the other equations with the
solution `(11/5)`  

`z = -3x + 2 (11/5) + 1`

`x = (3(11/5))/2 - 3/2`  

`y = 11/5`
 



Multiply `2`by each
term inside the parentheses.

`z = -3x + 22/5 + 1`

`x = (3(11/5))/2 - 3/2`  

`y = 11/5`


Combine `22/5 +
1`  into a single expression by finding the least common
denominator (LCD). The LCD of `22/5 +
1`  is `5` .

`z = -3x + 27/5`

`x = (3(11/5))/2
- 3/2`
 
`y = 11/5`  



Remove the
single term factors from the
expression.

`z = 27/5 - 3x`

 
`x = 33/10 - 3/2`

 
`y = 11/5`



Remove the parentheses from the
numerator.

`z = 27/5 - 3x`

`x = 18/10`  

`y = 11/5`
 



Combine `33/10 - 3/2`  into a single
expression by finding the least common denominator
(LCD). The LCD of `33/10 - 3/2`  is `10` .


`z = 27/5 - 3x`  

`x = 9 /5`  

`y = 11/5`


Since the
equation was solved for `x` , replace all occurrences of `x`in the other
equations with the solution `(9/5)`

`z
= 27/5 - 3(9/5)`  

`x = 9/5`  

`y =
11/5`


Multiply `-3`by each
term inside the parentheses.

`z = 27/5
- 27/5`  

`x = 9/5`  

`y = 11/5`



Combine all similar
expressions.

`z=0 `

`x =
9/5`  

`y = 11/5`


This is the
solution to the system of equations.


`z=0`

`x = 9/5`  

`y = 11/5`