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Show that the following system of equations has unique solutions. Find its solution by thereduction method𝑥 + 𝑦 + 𝑧 = 2, 𝑥 − 2𝑦 + 𝑧 = 8, 3𝑥 + 𝑦 + 𝑧 = 4

Question

Show that the following system of equations has unique solutions. Find its solution by the reduction method

The system of equations is:

  1. x+y+z=2 x + y + z = 2
  2. x2y+z=8 x - 2y + z = 8
  3. 3x+y+z=4 3x + y + z = 4

To find the unique solution using the reduction method:

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Solution

Sure, let's solve this system of equations step by step.

The system of equations is:

  1. x + y + z = 2
  2. x - 2y + z = 8
  3. 3x + y + z = 4

Step 1: Subtract the first equation from the second and third equations to eliminate x:

Subtracting equation 1 from equation 2 gives: -3y = 6, or y = -2. Subt

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This problem has been solved

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{2x+y=43x−y=-14{2𝑥+𝑦=43𝑥-𝑦=-14Which is the solution to the system of equations shown? (2, 0) (0, -2) (-2, 8) (-2, 0)

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