Question

Solve the system using the elimination method:2x - y + z = -26x + 3y - 4z = 8-3x + 2y + 3z = -6

Answer 1

multiply 2x - y + z = - 2 for 3

`6x-3y+3z=-6`

then sunstract the equation 1 and 2

`\begin{gathered} 6x+3y-4z=8 \\ 6x-3y+3z=-6 \\ 6y-7z=14 \end{gathered}`

multiply -3x+2y+3z=-6 for 2

`-6x+4y+6z=-12`

adding

`\begin{gathered} -6x+4y+6z=-12 \\ \underline{6x-3y+3z=-6} \\ y+9z=-18 \end{gathered}`

multiply y+9z=-18 for 6

`6y+54z=-108`

Subtracting

`\begin{gathered} 6y+54z=-108 \\ \underline{6y-7z=14} \\ 61z=-122 \end{gathered}`

then solve

`\begin{gathered} 61z=-122 \\ (61z)/(61)=(-122)/(61) \\ z=-2 \end{gathered}`
`\begin{gathered} 6y-7\mleft(-2\mright)=14 \\ 6y+14=14 \\ 6y+14-14=14-14 \\ 6y=0 \\ y=0 \end{gathered}`
`\begin{gathered} 6x-3\cdot\: 0+3\mleft(-2\mright)=-6 \\ 6x-6=-6 \\ 6x-6+6=-6+6 \\ 6x=0 \\ x=0 \end{gathered}`

answer is: x = 0, y = 0 and z = - 2