Question

\(\dfrac{x}{y}=\dfrac{5}{7}\) và 2x+3y=33

Answer 1

Ta có: \(\dfrac{x}{y}=\dfrac{5}{7}\Leftrightarrow\dfrac{x}{5}=\dfrac{y}{7}\)

Áp dụng định luật bảo toàn khối lượng, ta có:

\(\dfrac{x}{5}=\dfrac{y}{7}\Leftrightarrow\dfrac{2x}{10}=\dfrac{3y}{21}=\dfrac{2x+3y}{10+21}=\dfrac{33}{31}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{165}{31}\\y=\dfrac{231}{31}\end{matrix}\right.\)

Answer 2

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

áp dụng t/c dtsbn ta có:

\(\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{2x+3y}{5.2+3.7}=\dfrac{33}{31}\)

\(\dfrac{x}{5}=\dfrac{33}{31}\Rightarrow x=\dfrac{165}{31}\\ \dfrac{y}{7}=\dfrac{33}{31}\Rightarrow y=\dfrac{231}{31}\)