1. Cramer’s Rule for 2x2 systems
Jerry, I'm at the corner of 1st and 1st. Wait a minute, how can a street intersect itself? I must be at the nexus of the universe!

2. Actually, Gabriel Cramer was a Swiss mathematician (1704 -1752)
Cramer’s Rule
Actually, Gabriel Cramer was a Swiss mathematician ( )

3. Coefficient Matrices
You can use determinants to solve a system of linear equations.
You use the coefficient matrix of the linear system.
Linear System Coeff Matrix ax+by=e cx+dy=f

4. Cramer’s Rule for 2x2 System
Let A be the coefficient matrix
Linear System Coeff Matrix ax+by=e cx+dy=f
If detA 0, then the system has exactly one solution:
and

5. Example 1- Cramer’s Rule 2x2
Solve the system:
8x+5y=2
2x-4y=-10
The coefficient matrix is:
and
So:
and

6. Solution: (-1,2)

7. Example 2- Cramer’s Rule 2x2
Solve the system:
2x+y=1
3x-2y=-23
The solution is: (-3,7) !!!

8. Example 3- Cramer’s Rule 2x2
Solve the system:
5x+2y=8
2x-3y= 7
The solution is: (2,-1) !!!