Chapter 5, Systems of Equations and Inequalities - Section 5.4 - Systems of Nonlinear Equations - 5.4 Exercises - Page 466: 31

$(\frac{1}{5},\frac{1}{3})$

Let $1/x=a,1/y=b$ Then our system of equations is: $\{2a-3b=1, -4a+7b=1\}$. Adding twice the first equation to the second one, we get: $b=3$ Plugging this back into the first equation, we get: $2a-3(3)=1\\2a=10\\a=5$ Hence, the solutions are: $(\frac{1}{5},\frac{1}{3})$