Toán Lớp 7: a)x/y/z=3/5/(-2) và 5x-y+3z=124
b) x-1/2=y-2/3=z-3/4 và x-2y+3z=14
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Toán Lớp 7: a)x/y/z=3/5/(-2) và 5x-y+3z=124
b) x-1/2=y-2/3=z-3/4 và x-2y+3z=14
Comments ( 2 )
a)x:y:z = 3:5:\left( { – 2} \right)\\
\Leftrightarrow \dfrac{x}{3} = \dfrac{y}{5} = \dfrac{z}{{ – 2}} = \dfrac{{5x}}{{15}} = \dfrac{{3z}}{{ – 6}}\\
= \dfrac{{5x – y + 3z}}{{15 – 5 + \left( { – 6} \right)}} = \dfrac{{124}}{4} = 31\\
\Leftrightarrow \left\{ \begin{array}{l}
x = 31.3 = 93\\
y = 31.5 = 155\\
z = 31.\left( { – 2} \right) = – 62
\end{array} \right.\\
Vậy\,x = 93;y = 155;z = – 62\\
b)\dfrac{{x – 1}}{2} = \dfrac{{y – 2}}{3} = \dfrac{{z – 3}}{4}\\
= \dfrac{{2\left( {y – 2} \right)}}{6} = \dfrac{{3\left( {z – 3} \right)}}{{12}}\\
= \dfrac{{x – 1 – 2\left( {y – 2} \right) + 3\left( {z – 3} \right)}}{{2 – 6 + 12}}\\
= \dfrac{{x – 1 – 2y + 4 + 3z – 9}}{8}\\
= \dfrac{{x – 2y + 3z – 1 + 4 – 9}}{8}\\
= \dfrac{{14 – 6}}{8} = 1\\
\Leftrightarrow \left\{ \begin{array}{l}
x – 1 = 2\\
y – 2 = 3\\
z – 3 = 4
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 3\\
y = 5\\
z = 7
\end{array} \right.\\
Vậy\,x = 3;y = 5;z = 7
\end{array}$