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faust18 [17]
3 years ago
14

4x-y+2z=-6,-2x+3y-z=8,2y+3z=-5

Mathematics
1 answer:
Anit [1.1K]3 years ago
5 0
From third equation count y:
2y+3z=-5 \\ 2y=-5-3z \qquad /:2 \\ y=\frac{-5-3z}{2}
From first equation count x:
4x-y+2z=-6 \\ 4x=-6-2z+y \qquad /:4 \\ x=\frac{-6-2z+y}{4}
Substitute "y", which is counted from third equation:
x=\frac{-6-2z+\frac{-5-3z}{2}}{4}=\frac{-\frac{12}{2}-\frac{4z}{2}+\frac{-5-3z}{2}}{4}=\frac{-12-4z-5-3z}{8}=\frac{-7z-17}{8}
So now you've got:
y=\frac{-5-3z}{2} \\ x=\frac{-z-7}{8} \ \\ \hbox{Substitute this to second equation:} \\  -2 \cdot \frac{-7z-17}{8}+3 \cdot \frac{-5-3z}{2}-z=8  \\ \frac{7z+17}{4}+\frac{-15-9z}{2}-z=8 \qquad /\cdot 4 \\ 7z+17-30-18z-4z=32 \\ -15z-13=32 \\ -15z=45 \qquad /:(-15) \\ z=-3 \\ x=\frac{3-7}{8}=\frac{4}{8}=\frac{1}{2} \\ y=\frac{-5+9}{2}=\frac{4}{2}=2
So the solution is:
\begin{cases} x=\frac{1}{2} \\ y=2 \\ z=-3 \end{cases}
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