x=72

y=60

z=30

\(5x=6y=9z\Leftrightarrow\frac{x}{\frac{1}{5}}=\frac{y}{\frac{1}{6}}=\frac{z}{\frac{1}{9}}\)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\frac{x}{\frac{1}{5}}=\frac{y}{\frac{1}{6}}=\frac{z}{\frac{1}{9}}=\frac{x+y+z}{\frac{1}{5}+\frac{1}{6}+\frac{1}{9}}=\frac{860}{\frac{43}{90}}=1800\)

\(\Rightarrow\begin{cases}x=1800.\frac{1}{5}=360\\y=1800.\frac{1}{6}=300\\z=1800.\frac{1}{9}=200\end{cases}\)

Vậy ..............

Theo đề, ta có

\(\frac{x}{3}=\frac{y}{5}=\frac{z}{-2}\) và 5x-y+3z= 124

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\frac{x}{3}=\frac{y}{5}=\frac{z}{-2}\left(=\right)\frac{5x}{15}=\frac{y}{5}=\frac{3z}{-6}=\frac{5x-y+3z}{15-5+\left(-6\right)}=\frac{124}{4}=31\)

=>  \(\frac{x}{3}=31\)

\(\frac{y}{5}=31\)

\(\frac{z}{-2}=31\)

=>  x = 93

y  = 155

z = -62

\(\frac{x}{3}\)\(=\)\(\frac{y}{5}\)\(=\)\(\frac{z}{-2}\) và  \(5x-y+3z=124\)

\(\frac{x}{3}\)\(=\)\(\frac{y}{5}\)\(=\)\(\frac{z}{-2}\)\(\left(=\right)\)\(\frac{5x}{15}\)\(=\)\(\frac{y}{5}\)\(=\)\(\frac{3z}{-6}\)\(=\)\(\frac{5x-y-3x}{15-5-\left(-6\right)}\)\(=\)\(\frac{124}{4}\)\(=\)\(31\)

\(\frac{x}{3}\)\(=\)\(31\)

\(\frac{y}{5}\)\(=\)\(31\)

\(\frac{x}{-2}\)\(=\)\(31\)

\(x=93\)

\(y=155\)

\(x=-62\)

a.

$7x-2y=5x-3y$

$\Leftrightarrow 2x=-y$. Thay vào điều kiện số 2 ta có:

$-y+3y=20$

$2y=20$

$\Rightarrow y=10$. 

$x=\frac{-y}{2}=\frac{-10}{2}=-5$

b.

$2x=3y\Rightarrow \frac{x}{3}=\frac{y}{2}$

$3y=4z-2y\Rightarrow 5y=4z\Rightarrow \frac{y}{4}=\frac{z}{5}$

$\Rightarrow \frac{x}{6}=\frac{y}{4}=\frac{z}{5}$

Áp dụng tính chất dãy tỉ số bằng nhau:

$\frac{x}{6}=\frac{y}{4}=\frac{z}{5}=\frac{x+y+z}{6+4+5}=\frac{45}{15}=3$

$\Rightarrow x=6.3=18; y=4.3=12; z=5.3=15$ 

c.

$3x=4y-2x$

$\Rightarrow 5x=4y\Rightarrow x=\frac{4}{5}y$

$3x=7z-4y$

$\Leftrightarrow \frac{12}{5}y=7z-4y$

$\Leftrightarrow \frac{32}{5}y=7z\Rightarrow z=\frac{32}{35}y$

Khi đó:

$x+y-2z=10$

$\frac{4}{5}y+y-2.\frac{32}{35}y=10$

$y.\frac{-1}{35}=10$

$y=-350$

$x=\frac{4}{5}y=\frac{4}{5}.(-350)=-280$

$z=\frac{32}{35}y=\frac{32}{35}.(-350)=-320$

bài 2 :

ta có x:y:z=3:5:(-2)

=>x/3=y/5=z/-2

=>5x/15=y/5=3z/-6

áp dụng tc dãy ... ta có :

5x/15=y/5=3z/-6=5x-y+3z/15-5+(-6)=-16/4=-4

=>x/3=-=>x=-12

=>y/5=-4=>y=-20

=>z/-2=-4=>z=8

Ta có:          \(\frac{x}{10}=\frac{y}{6}=\frac{z}{21}\Rightarrow\frac{5x}{50}=\frac{y}{6}=\frac{2z}{42}=\frac{5x+y-2z}{50+6-42}=\frac{28}{14}=2\)

Vậy:          \(\frac{x}{10}=2\Rightarrow x=2\times10=20\)

                   \(\frac{y}{6}=2\Rightarrow y=2\times6=12\)

                 \(\frac{z}{21}=2\Rightarrow z=2\times21=42\)

\(\frac{x}{10}=\frac{y}{6}=\frac{z}{21}\Rightarrow\frac{5x}{50}=\frac{y}{6}=\frac{2z}{42}\)

áp dụng tính chất của dãy tỉ số = nhau ta có:

\(\frac{5x}{50}=\frac{y}{6}=\frac{2z}{42}=\frac{5x+y-2z}{50+6-42}=\frac{28}{14}=2\)

suy ra \(\frac{5x}{50}=2\Rightarrow5x=100\Rightarrow x=20\)

\(\frac{y}{6}=2\Rightarrow y=12\)

\(\frac{2x}{42}=2\Rightarrow2x=84\Rightarrow x=42\)

áp dụng tc dãy tỉ số bằng nhau ta có 

x/10=y/6=z/21

=5x/10.5+y/6-z/21.2

=5x+y-z/14

=28/14

=2

=>x/10=2=>x=20

=>y/6=2=>y=12

=>z/21=2=>z=42

vay x=20,y=12,z=42 

Ta co : \(\frac{x}{10}=\frac{y}{6}=\frac{z}{21}\) va 5x + y - 2z = 28

\(\frac{x}{10}=\frac{y}{6}=\frac{z}{21}=\frac{5x}{50}=\frac{y}{6}=\frac{2z}{42}\)

\(\frac{5x}{50}=\frac{y}{6}=\frac{2z}{42}\) va 5x + y -2z

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\frac{5x}{50}=\frac{y}{6}=\frac{2z}{42}=\frac{5x+y-2z}{50+6-42}=\frac{28}{14}=2\)

Suy ra : \(\frac{5x}{50}=2\Rightarrow x=2.50:5=20\)

\(\frac{y}{6}=2\Rightarrow y=2.6=12\)

\(\frac{2z}{42}=2\Rightarrow z=2.42:2=42\)

Vậy : \(x=20;y=12;z=42\)