Answer:
[tex]x=\frac{49}{20}[/tex], [tex]y=-\frac{17}{8}[/tex]
Step-by-step explanation:
[tex]\left \{ {{\frac{x}{2}+\frac{y}{5}=\frac{4}{5}} \atop {\frac{x}{6}-\frac{y}{5}=\frac{5}{6}}} \right.[/tex]
[tex]\frac{x}{2}+\frac{x}{6}=\frac{4}{5}+\frac{5}{6}[/tex]
[tex]\frac{6x}{12}+\frac{2x}{12}=\frac{24}{30}+\frac{25}{30}[/tex]
[tex]\frac{8x}{12}=\frac{49}{30}[/tex]
[tex]240x=588[/tex]
[tex]x=\frac{49}{20}[/tex]
[tex]\frac{x}{2}+\frac{y}{5}=\frac{4}{5}[/tex]
[tex]\frac{\frac{49}{20}}{2}+\frac{y}{5}=\frac{4}{5}[/tex]
[tex]\frac{49}{40}+\frac{y}{5}=\frac{4}{5}[/tex]
[tex]\frac{49}{40}=\frac{4-y}{5}[/tex]
[tex]245=160-40y[/tex]
[tex]85=-40y[/tex]
[tex]y=-\frac{17}{8}[/tex]
