?For which value(s) of a does the following system have zero solutions? One solution?

Chapter 1, Problem 10

(choose chapter or problem)

For which value(s) of a does the following system have zero solutions? One solution? Infinitely many solutions?

$x_{1}+x_{2}+x_{3}=4$

$x_{3}=2$

$\left(a^{2}-4\right) x_{3}=a-2$

Equation Transcription:

${x}_{1}+{x}_{2}+{x}_{3}\ \ =4$

$\ {x}_{3}\ \ =2\$

$\left({{a}^{2}-4}\right){x}_{3}\ \ =a-2\$

Text Transcription:

x_1+x_2+x_3 =4

x_3 =2

(a^2-4)x_3 =a-2

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