Find the ordered quintuplet that satisfies the system of equations

$$\left[ \begin{array}{rcrcrcrcrcr}
a &+& 2b &+& 3c &+& 4d &+& 5e & = & 177,\\
2a &+& 3b &+& 4c &+& 5d &+& e & = & 154,\\
3a &+& 4b &+& 5c &+& d &+& 2e & = & 146,\\
4a &+& 5b &+& c &+& 2d &+& 3e & = & 138,\\
5a &+& b &+& 2c &+& 3d &+& 4e & = & 165.\end{array} \right] $\\$
\small{\text{
Inverse Matrix
$
\left[ \begin{array}{rcrcrcrcrcr}
-0.186667,& 0.013333,& 0.013333,& 0.013333,& 0.213333, \\
0.013333,& 0.013333,& 0.013333,& 0.213333,& -0.186667, \\
0.013333,& 0.013333,& 0.213333,& -0.186667,& 0.013333, \\
0.013333,& 0.213333,& -0.186667,& 0.013333,& 0.013333, \\
0.213333,& -0.186667,& 0.013333,& 0.013333,& 0.013333 \\
\end{array} \right]
$
}}\\\\
$ (a,b,c,d,e) = (8, 5, 12, 12, 15)$$$

on the top right hand corner of the web2 calc there is the work     "scientific"

Click on this and it brings up a drop down box.

Choose equations.

Choose 5 equations and 5 variables.

Enter your coefficients.  

I haven't tried it but I think that should work.