#### Answer

$(-3, 4)$ and $(4,-3)$

#### Work Step by Step

Step 1. From the first equation, we have
$y=1-x$
Step 2. Substitute for $y$ in the second equation. We have
$x^2+(1-x)^2=25$, $2x^2-2x-24=0$, or $x^2-x-12=0$
Step 3. Factoring the equation, we have
$(x-4)(x+3)=0$, thus $x=-3, 4$
Step 4. We can find the solutions as $(-3, 4)$ and $(4,-3)$
Step 5. Check the solutions and they fit both equations.