1. $\{(2,0)\}$

2. $\left\{x,4-{\displaystyle \frac{x}{2}}\right\}$

3. $\varnothing$

4. $\{(-5,0)\}$

5. $\{(6,8)\}$

6. $\{(-1,1),(4,16)\}$

7. $\left\{\left(-3,{\displaystyle \frac{1}{3}}\right),(2,2)\right\}$

8.

1. $\{\begin{array}{rcrrr}x& +& y& =& 485\\ x& -& y& =& 15\end{array}$

2. $x=250,y=235$

9. $x+{\displaystyle \frac{1}{2}}y+z=2y-{\displaystyle \frac{3}{4}}z={\displaystyle \frac{7}{4}}z={\displaystyle \frac{-27}{23}}$

10. $\{(1,3,5)\}$

11. $(7,3,-2)$

12. $\left(x,{\displaystyle \frac{2x}{3}}+{\displaystyle \frac{7}{3}},-x-1\right)$

13. $\left({\displaystyle \frac{1}{3}},-{\displaystyle \frac{4}{3}}+z,z\right)$

14. 53 nickels, 225 dimes, and 22 quarters

15. ${\displaystyle \frac{A}{(x-5)}}+{\displaystyle \frac{B}{(x+1)}}$

16. ${\displaystyle \frac{A}{x-2}}+{\displaystyle \frac{Bx+C}{x^2+1}}+{\displaystyle \frac{Dx+E}{{(x^2+1)}^2}}$

17. $-{\displaystyle \frac{10}{121(x+4)}}+{\displaystyle \frac{1}{11{(x+4)}^2}}+{\displaystyle \frac{10}{121(x-7)}}$

18.

19.

20. Maximum value is 6 at (3, 0).