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{\bf Question}

Find the value of $t$ for which the following system of equations
is consistent, and find the general solution in that case.
\begin{eqnarray*} w + 2x - y + 3z &amp; = &amp; 5 \\ 2w + 4x + y + 5z &amp; =
&amp; 12 \\ 3w + 6x + 3y + 7z &amp; = &amp; 19 \\ 7w + 14x + 2y + 18 z &amp; = &amp; t
\end{eqnarray*}

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{\bf Answer}

For consistency t = 41

$$\left( \begin{array}{c} 11  \\ 0 \\ 0 \\ -2\end{array} \right) +
p \left( \begin{array}{c} -2 \\ 1 \\ 0 \\ 0 \end{array} \right)+
q\left( \begin{array}{c} -8 \\ 0 \\ 1 \\ 3 \end{array} \right) $$


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