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# Putting It Together

After taking this module, you realize that you can create a system of linear equations based on the table you were given:
 Quantity for x Quantity for y Quantity for z Total on bill before taxes Invoice 1 1 5 6 1400 Invoice 2 2 4 8 1400 Invoice 3 4 3 12 1600

x + 5y + 6z = 1400

2x + 4y + 8z = 1400

4x + 3y + 12z = 1600

We should now be prepared to put this into a spreadsheet and have the technology do the calculations for us once we set up our equations:
 x y z 1 5 6 x = 1400 x 100 2 4 8 y = 1400 y 200 4 3 12 z = 1600 z 50
This gives us our solution that Product x costs $100, Product y costs$200 and Product z costs \$50. You are now able to complete your report for the meeting tomorrow. Notice that our 3x3 matrix (we’ll call this matrix A) contains the coefficients on the left-hand-side of our equation. The 1x3 matrix (we’ll call this matrix B) contains the total from the bills. To get our final answers we need to use the inverse matrix operation and multiply that inverse matrix by our Matrix B. The command to do this is =mmult(minverse(A),B) A couple of things to remember: we can name matrices (there is a video which shows you how to do that), and we need to remember to hit Control-Shift-Enter when we are done with our equation and not just Enter.