Solve the system of equations.
-$\frac{6}{y}+\frac{2}{x}=\frac{23}{20}$
$\frac{4}{y}-\frac{2}{x}=\frac{1}{10}$

A) $\{(5,8\})$

B) $\varnothing$

C) $\{(-5,8\})$

D) $\left\{\left\{\left(\frac{1}{5}, \frac{1}{8}\right)\right\}\right.$

Question

Solve the system of equations.
-$\frac{6}{y}+\frac{2}{x}=\frac{23}{20}$
$\frac{4}{y}-\frac{2}{x}=\frac{1}{10}$

A) $\{(5,8\})$

B) $\varnothing$

C) $\{(-5,8\})$

D) $\left\{\left\{\left(\frac{1}{5}, \frac{1}{8}\right)\right\}\right.$

Quizplus · Accepted Answer

Adding the two equations eliminates the $\frac{2}{x}$ term, resulting in $\frac{10}{y} = \frac{12}{10}$ or $y = \frac{25}{3}$, which does not match any of the provided solutions. However, solving the system correctly, we find $x = 5$ and $y = 8$, which corresponds to choice A. My initial explanation contained a calculation mistake. The correct approach involves solving the system of equations directly, leading to the solution $x = 5$ and $y = 8$.