Ahyllin
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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

Respuesta :

nktselepov

[tex]\begin{equation*} \begin{cases} 2x+y-z=0 \\ x -y+z=6 \\ x +2y+z=3 \end{cases}\end{equation*}[/tex]

[tex]\begin{equation*} \begin{cases} 2x+y-z=0 \\ -x +y-z=-6 \\ -x -2y-z=-3 \end{cases}\end{equation*}[/tex]

Adding all 3 equations

[tex]-3z=-9\\z=3[/tex]

[tex]\begin{equation*} \begin{cases} 2x+y=3 \\ -x +y=-3 \\ -x -2y=0 \end{cases}\end{equation*}[/tex]

Let's Express y by x

[tex]\begin{equation*} \begin{cases} y=3-2x \\ -x +y=-3 \\ -x -2y=0 \end{cases}\end{equation*}[/tex]

Substitute y in the 2nd equation

[tex]x+3-2x=-3\\-3x=-6\\x=2[/tex]

Now find y

[tex]-2+y=-3\\y=-1[/tex]

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

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

Peaches2805
Answer: C) x = 2, y = -1, z = 3

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