Chapter 9.2, Problem 5CVC

Using Gaussian elimination to solve

$\{\begin{array}{l}3x+2y-2z=0\\ x-y+z=5,\end{array}$

we obtain the matrix

$\left[\begin{array}{lll}1\hfill & -1\hfill & 1\hfill \\ 0\hfill & 1\hfill & -1\hfill \end{array}|\begin{array}{l}5\\ -3\end{array}\right].$

Translating this matrix back into equation form gives

$\{\begin{array}{l}\_\_\_\_\_\_\text{Equation 1}\\ \_\_\_\_\_\_\text{Equation 2}\end{array}$

Solving Equation 2 for y in terms of z. results in $y=$

_____Substituting this expression for y in Equation 1 gives $x=$

________ The system’s solution

set is____________.