Theo bài ra: \(\dfrac{1+5y}{24}=\dfrac{1+7y}{7x}=\dfrac{1+9y}{2x}\left(1\right)\)

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

\(\dfrac{1+5y}{24}=\dfrac{1+7y}{7x}=\dfrac{1+9y}{2x}=\dfrac{-2y}{24-7x}=\dfrac{-2y}{5x}\)

TH1: \(y=0\)

\(\Rightarrow\left(1\right)\Rightarrow\dfrac{1}{24}=\dfrac{1}{7x}=\dfrac{1}{2x}\) (vô lí)

\(\Rightarrow\) Loại

TH2: \(y\ne0\)

\(\Rightarrow\dfrac{-2y}{24-7x}=\dfrac{-2y}{5x}\)

\(\Rightarrow24-7x=5x\)

\(\Rightarrow12x=24\)

\(\Rightarrow x=2\)

Thay \(x=2\) vào \(\dfrac{1+5y}{24}=\dfrac{1+7y}{7x}\) , ta được:

\(\dfrac{1+5y}{24}=\dfrac{1+7y}{14}\)

\(\Rightarrow\left(1+5y\right)14=\left(1+7y\right)24\)

\(\Rightarrow14+70y=24+168y\)

\(\Rightarrow70y-168y=24-14\)

\(\Rightarrow-98y=10\)

\(\Rightarrow y=-\dfrac{5}{49}\)

Vậy \(x=2;y=-\dfrac{5}{49}\)

\(\frac{1+7y}{7x}=\frac{1+9y}{2x}\) \(\Leftrightarrow\frac{1+7y}{7}=\frac{1+9y}{2}\)

\(\Leftrightarrow\left(1+7y\right)2=7\left(1+9y\right)\)

\(\Leftrightarrow2+14y=7+63y\)

\(\Leftrightarrow63y-14y=2-7\)

\(\Leftrightarrow y=-\frac{5}{49}\)

Thay \(x=-\frac{5}{49}\) vào biểu thức ta có :

\(\frac{1+7.\frac{-5}{49}}{7.x}=\frac{1+9.\frac{-5}{49}}{2x}\)

\(\Leftrightarrow x=2\)

Vậy..

Lời giải:

Ta có:
\(\frac{1+7y}{7x}=\frac{1+9y}{2x}\Rightarrow \frac{1+7y}{7}=\frac{1+9y}{2}\)

\(\Rightarrow 2(1+7y)=7(1+9y)\)

\(\Leftrightarrow 49y+5=0\Rightarrow y=\frac{-5}{49}\). Thay giá trị trên của $y$ vào điều kiện ban đầu ta có:

\(\frac{1+5y}{24}=\frac{1+9y}{2x}\)

\(\Leftrightarrow \frac{1+5.\frac{-5}{49}}{24}=\frac{1+9.\frac{-5}{49}}{2x}\)

\(\Leftrightarrow x=4\)

Vậy \(x=4; y=\frac{-5}{49}\)

\(\dfrac{1+7y}{7x}=\dfrac{1+9y}{2x}\Rightarrow\dfrac{2+14y}{14x}=\dfrac{7+63y}{14x}\)

\(\Rightarrow2+14y=7+63y\Rightarrow49y=-5\Rightarrow y=\dfrac{-5}{49}\)

\(\Rightarrow\dfrac{1+5\left(\dfrac{-5}{49}\right)}{24}=\dfrac{1+7\left(\dfrac{-5}{49}\right)}{7x}\)

\(\Rightarrow\dfrac{1}{49}=\dfrac{2}{49x}\Rightarrow x=2\)

Vậy \(\left\{{}\begin{matrix}x=2\\y=\dfrac{-5}{49}\end{matrix}\right.\)

câu hỏi tương tự có đó

\(\frac{1+4y}{18}=\frac{1+5y}{24}\Rightarrow24+96y=18+90y\)

\(\Rightarrow6+6y=0\Leftrightarrow6\left(1+y\right)=0\)Vậy y = -1

Thay y = -1 ta có :

\(\frac{1-5}{24}=\frac{1-6}{6x}\Leftrightarrow\frac{-5}{30}=-\frac{5}{6x}\left(\frac{-4}{24}=-\frac{5}{30}=\frac{1-5}{24}\right)\)

Vậy 6x = 30 hay x = 5