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:
To find the unique solution using the reduction method:
Solution
Sure, let's solve this system of equations step by step.
The system of equations is:
- x + y + z = 2
- x - 2y + z = 8
- 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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