Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 3y – 2z = 1 2х — у + 2z %3 3 4x + 5y + (a² – 11)z = a + 2 For a i there is no solution. For a - i there are infinitely many solutions. For at+ i the system has exactly one solution.

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.1: Systems Of Two Linear Equations In Two Variables
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Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions.
x + 3y – 2z = 1
2x – y + 2z = 3
%3D
4x + 5y + (a2 – 11)z = a + 2
For a = i
there is no solution.
For a = i
there are infinitely many solutions.
For at+ i
the system has exactly one solution.
Transcribed Image Text:Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 3y – 2z = 1 2x – y + 2z = 3 %3D 4x + 5y + (a2 – 11)z = a + 2 For a = i there is no solution. For a = i there are infinitely many solutions. For at+ i the system has exactly one solution.
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