Determine all equilibrium solutions (i.e., constant solutions that other solutions approach as $t \to \infty$) of the following nonhomogeneous linear system:

$$\displaystyle \ \boldsymbol{\vec{y}^{\, \prime}}(t) = \left\lbrack \begin{array}{rr} -4 & 4 \\ 4 & -4 \end{array} \right\rbrack \boldsymbol{\vec{y}}(t) + \left\lbrack \begin{array}{c} 1 \\ -1 \end{array} \right\rbrack.$$

As $t \to \infty$, the equilibrium solution has the form

$\boldsymbol{\vec{y}} =$

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$+ \ c$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$