Đáp án:
a)
Giải thích các bước giải:
a)
$\frac{x}{2}=\frac{y}{5}\Rightarrow x=\frac{2y}{5}$
$\frac{y}{5}=\frac{z}{7}\Rightarrow z=\frac{7y}{5}$
$2x+y-z=2 \Leftrightarrow 2.\frac{2y}{5}+y-\frac{7y}{5}=2$
$\Leftrightarrow \frac{2y}{5}=2 \Leftrightarrow y= 5$
$\Rightarrow x=\frac{2.5}{5}=2$
$\Rightarrow z= \frac{7.5}{5}=7$
b)
$\frac{x}{5}=\frac{y}{7}\Rightarrow x=\frac{5y}{7}\\
\frac{y}{7}=\frac{z}{3}\Rightarrow z=\frac{7y}{3}\\
4x-7z=-2 \Leftrightarrow 4.\frac{5y}{7}-7.\frac{7y}{3}=-2\\
\Leftrightarrow \frac{-283y}{21}=-2 \Leftrightarrow y= \frac{42}{283}\\
\Rightarrow x=\frac{5.\frac{42}{283}}{7}=\frac{30}{283}\\
\Rightarrow z= \frac{7.\frac{42}{283}}{3}=\frac{98}{283}$
c)
$2x=3y\Rightarrow x=\frac{3y}{2}\\
3y=4z\Rightarrow z=\frac{3y}{4}\\
x+y-z=21\Leftrightarrow \frac{3y}{2}+y-\frac{3y}{4}=21\\
\Leftrightarrow \frac{7y}{4}=21 \Leftrightarrow y= 12\\
\Rightarrow x=\frac{3.12}{2}=18\\
\Rightarrow z= \frac{3.12}{4}=9$
d)
$x=2y\\
3y=4z\Rightarrow z=\frac{3y}{4}\\
x+y+z=60\Leftrightarrow 2y+y+\frac{3y}{4}=60\\
\Leftrightarrow \frac{15y}{4}=60 \Leftrightarrow y= 16\\
\Rightarrow x=2.16=32\\
\Rightarrow z= \frac{3.16}{4}=12$
e)
$\frac{x}{2}=\frac{y}{-3}\Rightarrow x=\frac{2y}{-3}\\
\frac{y}{-3}=\frac{z}{4}\Rightarrow z=\frac{4y}{-3}\\
x-y=20\Leftrightarrow \frac{2y}{-3}-y=20\\
\Leftrightarrow \frac{-5y}{3}=20 \Leftrightarrow y= -12\\
\Rightarrow x=\frac{2.(-12)}{-3}=8\\
\Rightarrow z=\frac{4(-12)}{-3}=16$
