1. $x=3\text{,}y=2$

2. $x=5\text{,}y=-3$

3. $x=-4\text{,}y=3$

4. $x=5\text{,}y=4$

5. Inconsistent—no solution

6. Inconsistent—no solution

7. $x=-10+4t\text{,}y=t$ (infinitely many solutions)

8. $x=4+2t\text{,}y=t$ (infinitely many solutions)

9. $x=4\text{,}y=-1\text{,}z=3$

10. $x=3\text{,}y=1\text{,}z=-2$

11. $x=1\text{,}y=3\text{,}z=-4$

12. $x=1\text{,}y=3\text{,}z=5$

13. $x=y=z=0$

14. $x=5\text{,}y=3\text{,}z=-4$

15. Inconsistent—no solution

16. Inconsistent—no solution

17. Inconsistent—no solution

18. Inconsistent—no solution

19. $x=8+3t\text{,}y=3+2t\text{,}z=t$ (infinitely many solutions)

20. $x=-5t\text{,}y=5+t\text{,}z=t$ (infinitely many solutions)

21. $x=3-2t\text{,}y=2+3t\text{,}z=t$ (infinitely many solutions)

22. $x=-4t\text{,}y=-5t\text{,}z=t$ (infinitely many solutions)

23. $y(x)=3\cos 2x+4\sin 2x$

24. $y(x)=5\cosh 3x+4\sinh 3x$

25. $y(x)=7e^{5x}+3e^{-5x}$

26. $y(x)=23e^{11x}+21e^{-11x}$

27. $y(x)=23e^{3x}+17e^{-5x}$

28. $y(x)=23e^{3x}-8e^{7x}$

29. $y(x)=52e^{x/2}-45e^{x/3}$

30. $y(x)=81e^{4x/3}-40e^{-7x/5}$

31. Suggestion: The two lines both pass through the origin.

32. Suggestion: Two distinct planes in space either are parallel or intersect in a straight line.

33. (a) No solution (b) A unique solution (c) No solution (d) No solution (e) A unique solution (f) Infinitely many solutions

34. (a) No solution (b) Infinitely many solutions (c) No solution (d) No solution (e) Infinitely many solutions (f) A unique solution