Find a value of k so that \displaystyle \left\lbrack \begin{array}{r} 1 \\ 1 \end{array} \right\rbrack e^{k t} is a solution to \displaystyle \boldsymbol{\vec{x}^{\,\prime}} = \left\lbrack \begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array} \right\rbrack \boldsymbol{\vec{x}}.

The value of x in this system of equations is 1. 3x + y = 9 y = –4x + 10 substitute the value of y in the first equation: combine like terms: apply the subtraction property of equality: apply the division property of equality: 3x + (–4x + 10) = 9 –x + 10 = 9 –x = –1 x = 1 what is the value of y?