Question

5.Solve:

2x + y - z = 0
x - y + z = 6
x + 2y + z = 3

Select the appropriate response
A) x=2 y=-1 z=-3
B) x=-3 y=5 z=2
C) x=2 y=-1 z=3

Answer 1

Answer: C) x = 2, y = -1, z = 3

Answer 2

`\begin{equation*} \begin{cases} 2x+y-z=0 \\ x -y+z=6 \\ x +2y+z=3 \end{cases}\end{equation*}`

`\begin{equation*} \begin{cases} 2x+y-z=0 \\ -x +y-z=-6 \\ -x -2y-z=-3 \end{cases}\end{equation*}`

Adding all 3 equations

`-3z=-9\\z=3`

`\begin{equation*} \begin{cases} 2x+y=3 \\ -x +y=-3 \\ -x -2y=0 \end{cases}\end{equation*}`

Let's Express y by x

`\begin{equation*} \begin{cases} y=3-2x \\ -x +y=-3 \\ -x -2y=0 \end{cases}\end{equation*}`

Substitute y in the 2nd equation

`x+3-2x=-3\\-3x=-6\\x=2`

Now find y

`-2+y=-3\\y=-1`

Answer: C) x=2, y=-1, z=3

Hello from Russia and sorry for my bad english:^)