1. Types of Systems

2. Inconsistent of consistent? Example 1: 3x – y = 2 6x – 2y = 3 Example 2: x + y = -2 x -2y = 7

3. Inconsistent or Consistent? Example 3: x + 2y + z = 1 -x – y + 2z = 0 y + 3z = 4

4. Dependent vs. Independent A system is dependent if it has infinitely many solutions. A system is independent if it has only one solution. An inconsistent system can NEVER be dependent or independent.

5. Dependent or Independent? Example 4: 5x + 2y = 3 10x + 4y = 6 Example 5: x – y = 2 x + y = 4

6. Can also determine graphically. Properties of a Linear System of Two Equations y= m₁x +b₁ and y = m₂ + b₂. DESCRIPTI ON Slopes and y- interceptsGraphsSolutions CONSISTENT m₁ ≠ m₂ Intersect in one point One DEPENDENT m₁ = m₂ and b₁ = b₂ Coincide Infinite number INCONSISTENT m₁ = m₂ and b₁ ≠ b₂ ParallelNone