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.