Đáp án:
\(\begin{array}{l}
a)\,\,x = 40;\,\,y = 60;\,\,z = 80\\
b)\,\,x = - 5;\,\,y = 6;\,\,z = 7
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\,\,\frac{x}{2} = \frac{y}{3} = \frac{z}{4}\,\,\,va\,\,x + y - z = 20\\
Ap\,\,dung\,\,tinh\,\,chat\,\,day\,\,ti\,\,so\,\,bang\,\,nhau\\
\frac{x}{2} = \frac{y}{3} = \frac{z}{4} = \frac{{x + y - z}}{{2 + 3 - 4}} = \frac{{20}}{1} = 20\\
\Rightarrow \left\{ \begin{array}{l}
x = 2.20 = 40\\
y = 3.20 = 60\\
z = 4.20 = 80
\end{array} \right.\\
b)\,\,xy = - 30;\,\,yz = 42;\,\,z - x = 12\\
\Rightarrow \frac{{xy}}{{yz}} = \frac{{ - 30}}{{42}} \Rightarrow \frac{x}{z} = - \frac{5}{7} \Rightarrow \frac{x}{5} = \frac{z}{{ - 7}}\\
Ap\,\,dung\,\,tinh\,\,chat\,\,day\,\,ti\,\,so\,\,bang\,\,nhau\\
\frac{x}{5} = \frac{z}{{ - 7}} = \frac{{z - x}}{{ - 7 - 5}} = \frac{{12}}{{ - 12}} = - 1\\
\Rightarrow \left\{ \begin{array}{l}
x = 5.\left( { - 1} \right) = - 5\\
z = - 7.\left( { - 1} \right) = 7
\end{array} \right.\\
xy = - 30 \Leftrightarrow - 5.y = - 30 \Leftrightarrow y = 6
\end{array}\)
