Perform one step of row reduction, in order to calculate the values for $x$ and $y$ by back substitution. Then calculate the values for $x$ and $y$. Also calculate the determinant of the original matrix.

( Note: since the determinant is unchanged by type 3 row operations, it will be easier to calculate the determinant of the row reduced matrix.) $$\left[\begin{array}{cc} 9 &16\cr 24 &1 \end{array}\right] \left\lbrack \begin{array}{c} x \\ y \end{array} \right\rbrack = \left[\begin{array}{c} -3\cr 2 \end{array}\right]$$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $9$ $16$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $0$

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

$=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $-3$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

$x =$
$y =$
$\mbox{det} =$