\(\begin{cases}x+\frac{25}{2}y=25\left(1\right)\\y=\frac{x^2}{50}\left(2\right)\end{cases}\)\(\left(1\right)\Leftrightarrow\frac{25}{2}y=25-x\)
\(\Leftrightarrow y=\left(25-x\right):\frac{25}{2}\)
\(\Leftrightarrow y=25:\frac{25}{2}-x:\frac{25}{2}\)
\(\Leftrightarrow y=2-\frac{2x}{25}\).Thay pt (2) vào (1) được:
\(2-\frac{2x}{25}=\frac{x^2}{50}\)
\(\Leftrightarrow\frac{50-x}{25}=\frac{x^2}{50}\Rightarrow50\cdot\left(50-x\right)=x^2\cdot25\)
\(\Leftrightarrow250\cdot50=x^2\cdot25\)
\(\Leftrightarrow12500=25x^2\)
\(\Leftrightarrow x^2=500\Leftrightarrow x=\pm\sqrt{500}\)
Thay x vào (2) ta có:\(y=\frac{\pm\sqrt{500}^2}{50}=\pm10\)
