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Solving Systems of Equations

This guide provides a clear understanding of how to solve systems of equations using Cramer’s Rule, a method that utilizes determinants. We demonstrate the solution for the given system of equations: 5x + 2y = 16 and 3x - 5y = -9. Step-by-step, you'll learn to evaluate determinants to find the values of x and y, ultimately yielding the solution (2, 3). It is ideal for high school students looking to enhance their mathematical skills and problem-solving abilities.

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Solving Systems of Equations

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  1. Solving Systems of Equations Cramer’s Rule By Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: October 11, 2005

  2. Cramer’s Rule uses determinants to solve the system jeff.bivin@lz95.org

  3. System to be solved 5x + 2y = 16 3x – 5y = -9 jeff.bivin@lz95.org

  4. 5x + 2y = 163x – 5y = -9 Solving for x Use determinants X = jeff.bivin@lz95.org

  5. 5x + 2y = 163x – 5y = -9 Solving for x x y Use determinants X = x y jeff.bivin@lz95.org

  6. 5x + 2y = 163x – 5y = -9 Solving for x x y X = x y jeff.bivin@lz95.org

  7. 5x + 2y = 163x – 5y = -9 Solving for x x y X = x y jeff.bivin@lz95.org

  8. 5x + 2y = 163x – 5y = -9 Solving for x x y X = x y jeff.bivin@lz95.org

  9. 5x + 2y = 163x – 5y = -9 Solving for x x y X = x y jeff.bivin@lz95.org

  10. 5x + 2y = 163x – 5y = -9 Solving for x x y X = x y jeff.bivin@lz95.org

  11. 5x + 2y = 163x – 5y = -9 Solving for x x y X = x y jeff.bivin@lz95.org

  12. 5x + 2y = 163x – 5y = -9 Solving for x x y X = x y jeff.bivin@lz95.org

  13. 5x + 2y = 163x – 5y = -9 Solving for x x y X = x y jeff.bivin@lz95.org

  14. 5x + 2y = 163x – 5y = -9 Solving for x X = = jeff.bivin@lz95.org

  15. 5x + 2y = 163x – 5y = -9 Solving for x Evaluate the determinants X = = jeff.bivin@lz95.org

  16. 5x + 2y = 163x – 5y = -9 Solving for x X = = jeff.bivin@lz95.org

  17. 5x + 2y = 163x – 5y = -9 Solving for x X = = = = jeff.bivin@lz95.org

  18. now solve for y jeff.bivin@lz95.org

  19. 5x + 2y = 163x – 5y = -9 Solving for y y = jeff.bivin@lz95.org

  20. 5x + 2y = 163x – 5y = -9 Solving for y Use determinants y = jeff.bivin@lz95.org

  21. 5x + 2y = 163x – 5y = -9 Solving for y x y Use determinants y = x y jeff.bivin@lz95.org

  22. 5x + 2y = 163x – 5y = -9 Solving for y x y y = x y jeff.bivin@lz95.org

  23. 5x + 2y = 163x – 5y = -9 Solving for y x y y = x y jeff.bivin@lz95.org

  24. 5x + 2y = 163x – 5y = -9 Solving for y x y y = x y jeff.bivin@lz95.org

  25. 5x + 2y = 163x – 5y = -9 Solving for y x y y = x y jeff.bivin@lz95.org

  26. 5x + 2y = 163x – 5y = -9 Solving for y x y y = x y jeff.bivin@lz95.org

  27. 5x + 2y = 163x – 5y = -9 Solving for y x y y = x y jeff.bivin@lz95.org

  28. 5x + 2y = 163x – 5y = -9 Solving for y x y y = x y jeff.bivin@lz95.org

  29. 5x + 2y = 163x – 5y = -9 Solving for y y = jeff.bivin@lz95.org

  30. 5x + 2y = 163x – 5y = -9 Solving for y y = = jeff.bivin@lz95.org

  31. 5x + 2y = 163x – 5y = -9 Solving for y y = = jeff.bivin@lz95.org

  32. 5x + 2y = 163x – 5y = -9 Solving for y y = = = = jeff.bivin@lz95.org

  33. Final Result 5x + 2y = 16 3x – 5y = -9 x = 2 y = 3 (2,3) jeff.bivin@lz95.org

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