   SEARCH HOME Math Central Quandaries & Queries  Question from kareem, a student: my name is kareem and i am a student i have a math puzzle and i tried to solved it but it always have same mistake x-y=9 x+z=12 z-n=14 y+n=2 Hi Kareem,

I am not sure if you are working with equations

\begin{eqnarray*}
x&-&y && &&&=&9\\
x&&&+&z &&&=&12\\
&&&&z &-&n&=&14\\
&&y && &+&n&=&2
\end{eqnarray*}

or the rows of a matrix

$\left( \begin{array}{rrrrr}1&-1&0&0&9\\ 1&0&1&0&12\\ 0&0&1&-1&14\\ 0&1&0&1&2 \end{array} \right)$

In either case add -1 times the first equation (row) to the second equation (row) to obtain an equivalent system of equations (matrix). Next in the new system (matrix) add -1 times the second equation (row) to the fourth equation (row) to obtain an equivalent system of equations (matrix). Look at the third and fourth equations (rows). What does this tell you about $z$ and $n?$ What does this tell you about the system of equation in the problem?

Is this the type of result you got when you tried it?

Penny      Math Central is supported by the University of Regina and the Imperial Oil Foundation.