Ta có:\(\orbr{\begin{cases}2x-3y=3\\x+2y=2\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}4x-6y=6\\3x+6y=6\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}7x=12\\3x+6y=6\end{cases}}\)\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{12}{7}\\3x+6y=6\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=\frac{12}{7}\\y=\frac{1}{7}\end{cases}}\)

Vậy tỉ lệ thức \(\frac{y}{x}=\frac{1}{12}\)

SUY RA : (2X+3)(3X-1)=(5-X)(3-6X)

6x^2-2x+9x-3=15-30x-3x+6x^2

7x-3=15-33x

7x+33x=15+3

40x=18

x=18/40

x=9/20

Ta có:

\(\left(2x-3y\right).3=\left(x+2y\right).2\)

\(2x.3-3y.3=x.2+2y.2\)

\(6x-9y=2x+4y\)

\(6x-2x=9y+4y\)

\(4x=13y\)

Chia hai vế cho 4y, ta có:

\(\frac{4x}{4y}=\frac{13y}{4y}\)

\(=\frac{x}{y}=\frac{13}{4}\)

\(\Rightarrow\) Tỉ số giữa x và y là \(\frac{13}{4}\)

Ta có:

\(\frac{2x-3y}{x+2y}=\frac{2}{3}\)

<=> 3(2x-3y)= 2(x+2y)

<=> 6x - 9y = 2x + 4y

<=> 6x - 2x = 9y+4y

<=> 4x = 13y

=> \(\frac{x}{y}=\frac{13}{4}\)

khó nhỉ

\(\frac{x-1}{x+2}=\frac{x-2}{x+3}\)

=> (x-1).(x+3)=(x+2).(x-2)

=> x.(x-1)+3.(x-1)=x.(x-2)+2.(x-2)

=> x²-x+3x-3=x²-2x+2x-4

=> x²+2x-3=x²-4

=> 2x-3=4

=> 2x=7

=> x= 3,5

tỷ lệ thức tương đương:

(2x+3)(10x+2) = (5x+2)(4x+5)

=> 20x² + 30x + 4x + 6 =  20x² + 8x + 25x +10

=> 20x² + 30x + 4x - 20x² - 8x - 25x =   10 - 6

=> x = 4

Ta có: \(\frac{3x-y}{x+y}\)=\(\frac{3}{4}\)

\(\Leftrightarrow\)4(3x-y)=3(x+y)

\(\Leftrightarrow\)12x-4y=3x+3y

\(\Leftrightarrow\)12x-3x=4x+3y

\(\Leftrightarrow\)9x=7y

\(\Leftrightarrow\)\(\frac{x}{y}\)=\(\frac{7}{9}\)

\(\frac{3x-y}{x+y}=\frac{3}{4}\Leftrightarrow\frac{3x-y}{x+y}+1=\frac{3}{4}+1\Leftrightarrow\frac{4x}{x+y}=\frac{7}{4}.\) Ở vế trái chia cả tử và mẫu cho y , được:

\(\frac{4.\frac{x}{y}}{\frac{x}{y}+1}=\frac{7}{4}\)  Suy ra :  \(16.\frac{x}{y}=7\left(\frac{x}{y}+1\right)\) Vậy \(9.\frac{x}{y}=7\Leftrightarrow\frac{x}{y}=\frac{7}{9}\)