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Sagot :
Given the three variable simultaneous equations;
[tex]\begin{gathered} x+y+2z=-1\ldots\ldots.i \\ x+y+8z=-7\ldots\ldots.ii \\ x-9y-2z=-37\ldots\ldots.iii \end{gathered}[/tex]To solve;
let's solve for z by subtracting equation i from ii;
[tex]\begin{gathered} x+y+8z-(x+y+2z)=-7-(-1) \\ x-x+y-y+8z-2z=-7+1 \\ 6z=-6 \\ \frac{6z}{6}=\frac{-6}{6} \\ z=-1 \end{gathered}[/tex]next let's solve for y by subtracting equation i from iii;
[tex]\begin{gathered} x-9y-2z-(x+y+2z)=-37-(-1) \\ x-x-9y-y-2z-2z=-37+1 \\ -10y-4z=-36 \\ \text{ since z=-1} \\ -10y-4(-1)=-36 \\ -10y+4=-36 \\ -10y+4-4=-36-4 \\ -10y=-40 \\ \frac{-10y}{-10}=\frac{-40}{-10} \\ y=4 \end{gathered}[/tex]We have z and y, to get x let us substitute te values of y and z into equation i;
[tex]\begin{gathered} x+y+2z=-1 \\ x+(4)+2(-1)=-1 \\ x+4-2=-1 \\ x+2=-1 \\ x+2-2=-1-2 \\ x=-3 \end{gathered}[/tex]Therefore the values of x, y and z are;
[tex]\begin{gathered} x=-3 \\ y=4 \\ z=-1 \end{gathered}[/tex]Answer is A.
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