Chapter 5, Systems of Equations and Inequalities - Section 5.1 - Systems of Linear Equations in Two Variations - 5.1 Exercises - Page 447: 55

$x=-\frac{1}{a-1}, y=\frac{1}{a-1}$

We solve the first equation for $x$: $x+y=0$ We get: $x=-y$ Plugging this into the second equation, we get: $x+ay=1$ $-y+ay=1\\y(a-1)=1\\y=\frac{1}{a-1}$ Thus, we have $x=-y=-\frac{1}{a-1}$