Question

If: x+y+z=2-x+3y+2z=84x+y=4Find the value of x, y and z

Answer 1

We have

`\begin{gathered} x+y+z=2 \\ -x+3y+2z=8 \\ 4x+y=4 \end{gathered}`

We have with the third equation

`y=4-4x`

We substitute in the first and second equation

`\begin{gathered} x+4-4x+z=2 \\ -3x+z=-2 \end{gathered}`
`\begin{gathered} -x+3(4-4x)+2z=8 \\ -x+12-12x+2z=8 \\ -13x+2z=8-12 \\ -13x+2z=-4 \end{gathered}`

Then we have

`z=-2+3x`

We substitute

`\begin{gathered} -13x+2(-2+3x)=-4 \\ -13x-4-6x=-4 \\ -19x=0 \\ x=0 \end{gathered}`

if x=0

`z=-2`

and if x=0

`y=4`

ANSWER

x=0

y=4

z=-2