Cramer’s Rule and Solving Systems of Equations Chapter 2 Cramer’s Rule and Solving Systems of Equations

Cramer’s Rule Consider the system of equations below: If we take the system and make it look like below, then we can solve easily:

With our system rewritten, we can now solve for x and y by simply taking determinants.

Cramer’s Rule 2x2 EX 1: Solve using Cramer’s Rule 3x + 2y = 10

Determinants of 3x3 EX 3: Find the determinant of the following 3x3 matrix using the old-fashioned method. 4 5 8 -2 -3 1 0 2 -9

One More EX 4: Find the determinant of the following matrix 2 6 -10 2 6 -10 3 4 9 -1 -2 -6

Cramer’s Rule for 3x3 Cramer’s Rule for 3x3 matrices works EXACTLY like the rule for 2x2. We are going to replace the columns to solve.

Now that you’ve rewritten the system of three equations, you can find the determinants to give you x, y, and z.

Cramer’s Rule for 3x3 EX 5: Use Cramer’s Rule to solve the system of equations 3x – 2y + 4z = 10 4x + 6y – 5z = 20 5x – y + 2z = 30 EX 6: Use Cramer’s Rule to solve the system of equations 2x + 4z = 30 -x + y = -6 3y – 5z = 27

Assignment Chapter 2, Cramer’s Rule Cramer’s Rule, Matrix Equations Packet