Systems of Linear Equations

Part 4: Mixed Bag

For each of the following systems, determine the number of solutions to the system.

1. 2x₁ + 4x₂ = 6
   3x₁ + 6x₂ + 2x₃ = 7
   2x₁ + 4x₂ + 2x₃ = 4
   -2x₁ - 4x₂ + x₃ = -7

2. 2x₁ + 4x₂ = 6
   3x₁ + 6x₂ + 2x₃ = 7
   2x₁ + 4x₂ + 2x₃ = 4
   x₁ - 2x₂ = 5

3. 2x₁ + 4x₂ = 6
   3x₁ + 6x₂ + 2x₃ = 7
   2x₁ + 4x₂ + 2x₃ = 4
   2x₁ + 5x₂ = 8

4. 2x₁ + 4x₂ = 6
   3x₁ + 6x₂ + 2x₃ = 7
   2x₁ + 4x₂ + 2x₃ = 4
   x₁ + 2x₂ + 3x₃ = 3

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