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

\(\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{2x+3y-1}{6x}=\frac{2x+3y+1-2}{5+7}=\frac{2x+3y-1}{12}\)

\(\Rightarrow\frac{2x+3y-1}{12}=\frac{2x+3y-1}{6x}\)

TH 1 : \(2x+3y-1=0\)

\(\Rightarrow\frac{2x+1}{5}=0;\frac{3y-2}{7}=0\)

\(\Rightarrow2x+1=0;3y-2=0\)

\(\Rightarrow2x=-1;3y=2\)

\(\Rightarrow x=-\frac{1}{2};y=\frac{2}{3}\)

TH 2 : \(2x+3y-1\ne0\)

\(\Rightarrow6x=12\)

\(\Rightarrow x=2\)

Mà \(\frac{2x+1}{5}=\frac{3y-2}{7}\)

\(\Rightarrow\frac{2.2+1}{5}=\frac{3y-2}{7}\)

\(\Rightarrow1=\frac{3y-2}{7}\)

\(\Rightarrow3y-2=7\)

\(\Rightarrow3y=9\)

\(\Rightarrow y=3\)

Vậy \(\orbr{\begin{cases}x=-\frac{1}{2};y=\frac{2}{3}\\x=2;y=3\end{cases}}\)

Theo t/c dãy tỉ số bằng nhau :

\(\Rightarrow\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{2x+1+3y-2}{5+7}=\frac{2x+3y-1}{12}\)

Do \(\frac{2x+3y-1}{6x}=\frac{2x+3y-1}{12}\)

\(\Rightarrow6x=12\Leftrightarrow x=2\)

Xét :\(\frac{2x+1}{5}=\frac{3y-2}{7}\)

\(1=\frac{3y-2}{7}\)

\(\Rightarrow3y=9\Leftrightarrow y=3\)

ta có: \(\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{2x+1+3y-2}{5+7}=\frac{2x+3y-1}{12}\)

\(\Rightarrow\frac{2x+3y-1}{6x}=\frac{2x+3y-1}{12}\)

=> 6x = 12

x = 2

=>  \(\frac{2x+1}{5}=\frac{2.2+1}{5}=\frac{5}{5}=1\)

\(\frac{3y-2}{7}=1\Rightarrow3y-2=7\Rightarrow3y=9\Rightarrow y=3\)

KL: x = 2; y = 3

x=2

y=3

Áp dụng TC DCTSBN ta có :

\(\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{\left(2x+1\right)+\left(3y-2\right)}{5+7}=\frac{2x+3y-1}{12}=\frac{2x+3y-1}{6x}\)

\(\Rightarrow6x=12\Rightarrow x=2\)

Thay x = 2 và 2 TLT đầu ta được :

\(\frac{2.2+1}{5}=\frac{3y-2}{7}\)

\(\Leftrightarrow\frac{3y-2}{7}=1\)

\(\Rightarrow3y-2=7\Rightarrow y=3\)

Vậy x = 2 và y = 3

Ta có: \(\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{2x+3y-1}{6x}\) \(\left(x\ne0\right)\)

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

\(\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{2x+3y-1}{6x}\)\(=\frac{\left(2x+1\right)+\left(3y-2\right)-\left(2x+3y-1\right)}{5+7-6x}\)\(=\frac{0}{12-6x}=0\)

\(\Rightarrow\hept{\begin{cases}2x+1=0\\3y-2=0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=\frac{-1}{2}\\y=\frac{2}{3}\end{cases}}\)

\(\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{2x+3y-1}{6x}\)

\(\Rightarrow\frac{2x+1}{5}=k\rightarrow2x+1=5k\rightarrow2k=5k-1\)

\(\frac{3y-2}{7}=k\rightarrow3y-2=7k\rightarrow3y=2k+2\)

 \(\frac{2x+3y-1}{6x}=k\rightarrow2x+3y-1=6x.k\)

                                     \(\rightarrow5k-1+7k+2-1=k.3\left(5k-1\right)\)

                                     \(\rightarrow12k=15k^2-3k\)

                                      \(\rightarrow15k^2-15k=0\)

                                       \(\rightarrow15k\left(k-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}k=0\rightarrow x=\frac{-1}{2};y=\frac{2}{3}\\k=1\rightarrow x=2;y=3\end{cases}}\)

\(\frac{2x+1}{5}=\frac{3y-2}{7}=\frac{2x+3y-1}{6x}=\)

\(=\frac{2x+1+3y-2-2x-3y+1}{5+7-6x}=0\)

\(\Rightarrow\frac{2x+1}{5}=0\Rightarrow x=-\frac{1}{2}\)

\(\Rightarrow\frac{3y-2}{7}=0\Rightarrow y=\frac{2}{3}\)

Viết lại thành : \(\dfrac{x}{\dfrac{3}{2}}=\dfrac{y}{\dfrac{4}{3}}=\dfrac{z}{\dfrac{5}{4}}\)

Dựa theo tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x+y+z}{\dfrac{3}{2}+\dfrac{4}{3}+\dfrac{5}{4}}=\dfrac{49}{\dfrac{49}{12}}=12\)

-> x = \(12.\dfrac{3}{2}=18\)

y =\(12.\dfrac{4}{3}=16\)

z =\(12.\dfrac{5}{4}\) = 15

ai co nich truy kich co nhieu trang vinh vien