Question

Tìm các cặp số ( x , y) biết :

\(\dfrac{1+3y}{12}=\dfrac{1+5y}{5x}=\dfrac{1+7y}{4x}\)

Answer 1

\(\dfrac{1+5y}{5x}=\dfrac{1+7y}{4x}\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\4\left(1+5y\right)=5\left(1+7y\right)\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\15y=-1;y=-\dfrac{1}{15}\end{matrix}\right.\)

\(\dfrac{1+3y}{12}=\dfrac{1+5y}{x}\Leftrightarrow\left\{{}\begin{matrix}x\ne0\\x=\dfrac{12\left(1+5y\right)}{1+3y}=4.5.\left(\dfrac{3+15y}{5+15y}\right)=4.5.\left(\dfrac{3-1}{5-1}\right)=10\end{matrix}\right.\)\(\left(x;y\right)=\left(10;-\dfrac{1}{15}\right)\)