1. Applying Determinants to solve Systems of Equations 2x2 & 3x3
Cramer’s Rule
Applying Determinants to solve
Systems of Equations
2x2 & 3x3

2. 2x2 Determinants
Det A = ad – cb

3. Cramer’s Rule for 2x2 Part 1 1. Extract Coefficients
2. Calculate Determinant of Original Matrix

4. Cramer’s Rule for 2x2 Part 2 (Solving for x)
Replace the 1st column of the coefficient matrix with the constant matrix.
Calculate the determinant of new matrix & divide by original determinant.

5. Cramer’s Rule for 2x2 Part 3 (Solving for y)
Replace the 2nd column of the coefficient matrix with the constant matrix.
Calculate the determinant of new matrix & divide by original determinant.

6. Cramer’s Rule for 2x2 Part 4
To check x and y, substitute 51 in for x and 30 in for y.

7. Ex #4 Solve

8. 3x3 Determinants

9. Cramer’s Rule for 3x3 Part 1 Extract coefficients.
Calculate Original Determinant (OD) of Matrix

10. Cramer’s Rule for 3x3 Part 2 (Solving for x)
Replace the 1st column of the coefficient matrix with the constant matrix.
Calculate the determinant of new matrix & divide by original determinant (15).

11. Cramer’s Rule for 3x3 Part 3 (Solving for y)
Replace the 2nd column of the coefficient matrix with the constant matrix.
Calculate the determinant of new matrix & divide by original determinant (15).

12. Cramer’s Rule for 3x3 Part 4 (Solving for z)
Replace the 3rd column of the coefficient matrix with the constant matrix.
Calculate the determinant of new matrix & divide by original determinant (15).

13. Cramer’s Rule for 3x3 Part 5
9. To check x and y, substitute 2.6 in for x, 2.2 in for y, and 0.2 in for z.