Question

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

tìm các cặp số ( x, y )

Answer 1

Áp dụng tính chất của dãy tỉ số bằng nhau

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

\(=\frac{1+3y+1+7y}{12+4x}=\frac{2+10y}{12+4x}\)

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

\(\Rightarrow\frac{1+5y}{5x}=\frac{1+5y}{6+2x}\)

\(\Rightarrow5x=6x+2x\)

\(\Rightarrow3x=6\)

\(\Rightarrow x=2\)

\(\Rightarrow\frac{1+3y}{12}=\frac{1+5y}{5x}=\frac{1+5y}{5.2}=\frac{1+5y}{10}\)

\(\Rightarrow\frac{1+3y}{12}=\frac{1+5y}{10}\)

\(\Rightarrow10\left(1+3y\right)=12\left(1+5y\right)\)

\(\Rightarrow10+30y=12+60y\)

\(\Rightarrow30y=-2\)

\(\Rightarrow y=-\frac{1}{15}\)

Vậy \(x=2;y=-\frac{1}{15}\)