3x-2y/4=z-2x/5=4y-3z/2 và x+2y-3z=-12 tìm x,y,z 25/09/2021 Bởi Claire 3x-2y/4=z-2x/5=4y-3z/2 và x+2y-3z=-12 tìm x,y,z
Đáp án: Giải thích các bước giải: $\begin{array}{l} \frac{{3x – 2y}}{4} = \frac{{z – 2x}}{5} = \frac{{4y – 3z}}{2} = \frac{{3x – 2y + z – 2x + 4y – 3z}}{{4 + 5 + 2}}\\ = \frac{{x + 2y – 2z}}{{11}} = \frac{{ – 12 + z}}{{11}}\\ xet\frac{{z – 2x}}{5} = \frac{{ – 12 + z}}{{11}} \Leftrightarrow 11z – 22x = – 60 + 5z \Leftrightarrow 6z = 22x – 60\\ \Leftrightarrow x = \frac{{3z + 30}}{{11}}\\ xet\frac{{3x – 2y}}{4} = \frac{{ – 12 + z}}{{11}} \Leftrightarrow 33x – 22y = – 48 + 4z \Leftrightarrow 33.\frac{{3z + 30}}{{11}} – 22y = – 48 + 4z\\ \Leftrightarrow 9z + 90 – 22y = – 48 + 4z \Leftrightarrow 5z + 138 = 22y \Leftrightarrow y = \frac{{5z + 138}}{{22}}\\ thayvaobtx + 2y – 3z = – 12\\ \Leftrightarrow \frac{{3z + 30}}{{11}} + 2.\frac{{5z + 138}}{{22}} – 3.z = – 12 \Rightarrow z = 12 \Rightarrow x = 6;y = 9 \end{array}$ Bình luận
Đáp án:
Giải thích các bước giải:
$\begin{array}{l}
\frac{{3x – 2y}}{4} = \frac{{z – 2x}}{5} = \frac{{4y – 3z}}{2} = \frac{{3x – 2y + z – 2x + 4y – 3z}}{{4 + 5 + 2}}\\
= \frac{{x + 2y – 2z}}{{11}} = \frac{{ – 12 + z}}{{11}}\\
xet\frac{{z – 2x}}{5} = \frac{{ – 12 + z}}{{11}} \Leftrightarrow 11z – 22x = – 60 + 5z \Leftrightarrow 6z = 22x – 60\\
\Leftrightarrow x = \frac{{3z + 30}}{{11}}\\
xet\frac{{3x – 2y}}{4} = \frac{{ – 12 + z}}{{11}} \Leftrightarrow 33x – 22y = – 48 + 4z \Leftrightarrow 33.\frac{{3z + 30}}{{11}} – 22y = – 48 + 4z\\
\Leftrightarrow 9z + 90 – 22y = – 48 + 4z \Leftrightarrow 5z + 138 = 22y \Leftrightarrow y = \frac{{5z + 138}}{{22}}\\
thayvaobtx + 2y – 3z = – 12\\
\Leftrightarrow \frac{{3z + 30}}{{11}} + 2.\frac{{5z + 138}}{{22}} – 3.z = – 12 \Rightarrow z = 12 \Rightarrow x = 6;y = 9
\end{array}$