Solving Systems of Equations with Cramer's Rule

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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.

Bildung

Solving Systems of
Equations
Cramer’s Rule

System to be solved:

5x + 2y = 16
3x – 5y = -9

5x + 2y = 16
3x – 5y = -9
16 2

-9 -5

5 2

3 -5

5x + 2y = 16
3x – 5y = -9
16

-9

5 2

3 -5

5x + 2y = 16
3x – 5y = -9
16 2

-9 -5
-80 — (-18) -62
-25 — 6 -31
5 2

3 -5 2

5x + 2y = 16
3x – 5y = -9
5 16

3 -9

5 2

3 -5

5x + 2y = 16
3x – 5y = -9
5 16

3 -9
-45 — 48 -93
-25 — 6 -31
5 2

3 -5 3

Final Result

5x + 2y = 16
3x – 5y = -9
x=2
y=3 (2,3)

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Solving Systems of Equations with Cramer's Rule

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

17.

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)

Solving Systems of Equations with Cramer's Rule

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Solving Systems of Equations with Cramer's Rule