Problem:
Solution:
Take the sum of the the equations, we have:
$ \begin{eqnarray*} 2x + 3y - z &=& 1 \\ z &=& 2x + 3y - 1 \\ w &=& x + y + z - 2 \\ &=& x + y + (2x + 3y - 1) + 2 \\ &=& 3x + 4y + 1 \end{eqnarray*} $
Therefore the solutions are, in parameters $ s $ and $ t $, are
$ \left(\begin{array}{c}x \\ y \\ z \\ w \end{array}\right) = \left(\begin{array}{c}s \\ t \\ 2s + 3t - 1 \\ 3s + 4t + 1 \end{array}\right) $
Solution:
Take the sum of the the equations, we have:
$ \begin{eqnarray*} 2x + 3y - z &=& 1 \\ z &=& 2x + 3y - 1 \\ w &=& x + y + z - 2 \\ &=& x + y + (2x + 3y - 1) + 2 \\ &=& 3x + 4y + 1 \end{eqnarray*} $
Therefore the solutions are, in parameters $ s $ and $ t $, are
$ \left(\begin{array}{c}x \\ y \\ z \\ w \end{array}\right) = \left(\begin{array}{c}s \\ t \\ 2s + 3t - 1 \\ 3s + 4t + 1 \end{array}\right) $
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