Cramer’s Rule for 2x2 systems

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Presentation transcript:

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!

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

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

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

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

Solution: (-1,2)

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

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