Solving Systems of Equations

Cramer’s Rule

By

Jeffrey Bivin

Lake Zurich High School

jeff.bivin@lz95.org

Last Updated: October 11, 2005

Cramer’s Rule

uses determinants

to solve the system

jeff.bivin@lz95.org

System to be solved

5x + 2y = 16

3x – 5y = -9

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16

-9

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16 2

-9 -5

5 2

3 -5

-80 — (-18)

-25 — 6

jeff.bivin@lz95.org

-62

-31

2

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

5 16

3 -9

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

5 16

3 -9

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

5 16

3 -9

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

5 16

3 -9

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

5 16

3 -9

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

5 16

3 -9

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

16

-9

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

5 16

3 -9

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

5 16

3 -9

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

5 16

3 -9

5 2

3 -5

jeff.bivin@lz95.org

5x + 2y = 163x – 5y = -9

5 16

3 -9

5 2

3 -5

-45 — 48

-25 — 6

jeff.bivin@lz95.org

-93

-31

3

Final Result

5x + 2y = 16

3x – 5y = -9

x = 2

y = 3 (2,3) jeff.bivin@lz95.org