Description
The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination.
x | + | 2y | − | z | = | −10 |
x | + | z | = | 0 | ||
2x | − | y | − | z | = | −15 |
Explanation & Answer
subtract the first equation from the second one, then divide the second equation by -2; subtract the first equation multiplied by 2 from the third one:
x + 2y - z = -10
y - z = -5
-5y + z = 5
add the second equation multiplied by 5 to the third equation:
x + 2y - z = - 10
y - z = -5
- 4z = - 20
Then from the last equation z = -20/-4 = 5, from the second equation y = z -5 = 0, from the first equation
x = -2y + z - 10 = 0 + 5 - 10 = - 5
Answer: (-5, 0, 5).
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