Question #N721
If the system of equations $\begin{cases} 2x + 3y = 7 \\ x - 2y = 1 \end{cases}$ has solution $(x, y)$, what is the value of $x - y$ ?
A. -2
B. -1
C. 1
D. 2
Correct Answer is: B
To solve for $x - y$, we can multiply the second equation by 2, giving us $2x - 4y = 2$. Subtracting this equation from the first equation, we get $7y = 5$, so $y = \frac{5}{7}$. Substituting this value back into the equation $x - 2y = 1$, we get $x - 2(\frac{5}{7}) = 1$, so $x = \frac{19}{7}$. Therefore, $x - y = \frac{19}{7} - \frac{5}{7} = \frac{14}{7} = 2$.