The document describes using Cramer's rule to solve a system of two equations with two unknowns (5x + 2y = 16, 3x - 5y = -9). It shows setting up the equations in a matrix and calculating the determinants to find that the solutions are x=2 and y=3.

1. Solving Systems of
Equations
Cramer’s Rule

2. System to be solved:
5x + 2y = 16
3x – 5y = -9

3. 5x + 2y = 16
3x – 5y = -9

4. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
5 2
3 -5

5. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
5 2
3 -5

6. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
5 2
3 -5

7. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
5 2
3 -5

8. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
5 2
3 -5

9. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
5 2
3 -5

10. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
5 2
3 -5

11. 5x + 2y = 16
3x – 5y = -9
16
-9
5 2
3 -5

12. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
5 2
3 -5

13. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
5 2
3 -5

14. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
5 2
3 -5

15. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
5 2
3 -5

16. 5x + 2y = 16
3x – 5y = -9
16 2
-9 -5
-80 — (-18) -62
-25 — 6 -31
5 2
3 -5 2

18. 5x + 2y = 16
3x – 5y = -9

19. 5x + 2y = 16
3x – 5y = -9

20. 5x + 2y = 16
3x – 5y = -9

21. 5x + 2y = 16
3x – 5y = -9
5 16
3 -9
5 2
3 -5

22. 5x + 2y = 16
3x – 5y = -9
5 16
3 -9
5 2
3 -5

23. 5x + 2y = 16
3x – 5y = -9
5 16
3 -9
5 2
3 -5

24. 5x + 2y = 16
3x – 5y = -9
5 16
3 -9
5 2
3 -5

25. 5x + 2y = 16
3x – 5y = -9
5 16
3 -9
5 2
3 -5

26. 5x + 2y = 16
3x – 5y = -9
5 16
3 -9
5 2
3 -5

27. 5x + 2y = 16
3x – 5y = -9
16
-9
5 2
3 -5

28. 5x + 2y = 16
3x – 5y = -9
5 16
3 -9
5 2
3 -5

29. 5x + 2y = 16
3x – 5y = -9
5 16
3 -9
5 2
3 -5

30. 5x + 2y = 16
3x – 5y = -9
5 16
3 -9
5 2
3 -5

31. 5x + 2y = 16
3x – 5y = -9
5 16
3 -9
-45 — 48 -93
-25 — 6 -31
5 2
3 -5 3

32. Final Result
5x + 2y = 16
3x – 5y = -9
x=2
y=3 (2,3)