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:

$x+y-2z=10$

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

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

$y=-350$

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

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

a, 3x-(2x+1)\(=2\)

\(\Leftrightarrow3x-2x-1=2\)

\(\Leftrightarrow3x-2x=2+1\)

\(\Leftrightarrow x=3\)

a) \(3x-\left(2x+1\right)=2\)

\(3x-2x-1=2\)

\(x-1=2\)

\(x=3\)

vay \(x=3\)

\(2x=3y-2x\Leftrightarrow4x=3y\Leftrightarrow\dfrac{x}{3}=\dfrac{y}{4}\\ 3y-2x=5z\Leftrightarrow4x-2x=5z\Leftrightarrow2x=5z\Leftrightarrow\dfrac{x}{5}=\dfrac{z}{2}\\ \Leftrightarrow\dfrac{x}{15}=\dfrac{y}{20}=\dfrac{z}{6}=\dfrac{x-y+z}{15-20+6}=\dfrac{99}{1}=99\\ \Leftrightarrow\left\{{}\begin{matrix}x=1485\\y=1980\\z=594\end{matrix}\right.\)

Answer:

Đề ra:

\(2x=3y-2x=5z\)

\(\Rightarrow2x+2x=3y=5z\)

\(\Rightarrow4x=3y=5z\)

\(4x=3y\Rightarrow\frac{x}{3}=\frac{y}{4}\Rightarrow\frac{x}{15}=\frac{y}{20}\)

\(3y=5z\Rightarrow\frac{y}{5}=\frac{z}{3}\Rightarrow\frac{y}{20}=\frac{z}{12}\)

Áp dụng tính chất của dãy tỉ số bằng nhau

\(\frac{x}{15}=\frac{y}{20}=\frac{z}{12}=\frac{x-y+z}{15-20+12}=\frac{90}{7}\)

\(\Rightarrow\frac{x}{15}=\frac{99}{7}\Rightarrow x=\frac{1485}{7}\)

\(\Rightarrow\frac{y}{20}=\frac{99}{7}\Rightarrow y=\frac{1980}{7}\)

\(\Rightarrow\frac{z}{12}=\frac{99}{7}\Rightarrow z=\frac{1188}{7}\)

Tìm x, y, z biết \(\frac{x}{3}=\frac{y}{5}=\frac{z}{8}\) và 2x + y - x = 108

Giải

Từ \(\frac{x}{3}=\frac{y}{5}=\frac{z}{8}\) suy ra: \(\frac{2x}{6}=\frac{y}{5}=\frac{z}{8}\)

Theo đề bài, ta có:

\(\frac{2x}{6}=\frac{y}{5}=\frac{z}{8}\) và 2x + y - z = 108

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

\(\frac{2x}{6}=\frac{y}{5}=\frac{z}{8}=\frac{2x+y-z}{6+5-8}=\frac{108}{3}=36\)

Do đó: \(\frac{2x}{6}=36=>x=36\cdot6:2=108\)

\(\frac{y}{5}=36=>y=36\cdot5=180\)

\(\frac{z}{8}=36=>z=36\cdot8=288\)

Vậy \(\left\{\left(x;y;z\right)\right\}\in\left\{\left(108;180;288\right)\right\}\)

X/4=y/5=z/6

=>2x/8=y/5=z/6

Áp dung... ta có:

2x/8=y/5=z/6=(2x+y-z)/(8+5-6)=14/7=2

Từ 2x/8=2=>2x=16=>x=8

Y/5=2=>y=10

Z/6=2=>z=12

Tick nhé

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