Solve for variables using multiple equations

[yashgupta25]

Hi

I need to find the value of 3 variables (x,y,z) in the format of Ax + By + Cz = D. The problem is my equation set contains around 35 equations (up to A₃₅x+B₃₅y+C₃₅z=D₃₅.

How do I get the best solution for (x,y,z) from this. The value are given below. Sheet also attached.Multiple variable solve.xlsx

Also, is the basic solution for (x,y,z) adequate, or some kind of a regression model is required?

Thanks in advance

A B C D
0.06 0.12 0.40 4.30
0.25 0.26 0.00 7.20
0.30 0.51 0.00 7.30
0.40 0.19 0.14 7.50
0.00 0.00 0.67 5.80
0.30 0.34 0.00 7.50
0.25 0.48 0.00 7.60
0.09 0.05 0.43 6.00
0.13 0.27 0.38 6.80
0.33 0.49 0.00 7.60
0.60 0.27 0.00 7.80
0.12 0.05 0.47 6.90
0.54 0.05 0.34 6.10
0.82 0.07 0.00 8.00
0.66 0.10 0.08 8.10
0.08 0.08 0.73 6.30
0.76 0.15 0.00 7.70
0.81 0.14 0.00 8.20
0.18 0.00 0.50 7.70
0.00 0.00 0.58 5.90
0.83 0.04 0.00 7.70
0.55 0.15 0.10 8.30
0.00 0.00 0.84 6.60
0.45 0.13 0.00 8.10
0.69 0.09 0.00 8.30
0.22 0.08 0.40 8.40
0.10 0.03 0.75 5.80
0.60 0.17 0.03 8.40
0.00 0.00 0.82 6.70
0.00 0.00 0.84 5.50
0.00 0.00 0.88 5.60
0.50 0.11 0.15 7.90
0.75 0.09 0.00 8.60
0.44 0.21 0.03 8.70

[Pete_UK]

I don't think your basic equation is adequate for this. If you apply filters to the data and select A=0, you will find that there are 6 rows of data that satisfy this criteria, and that B is also equal to zero, so you have a direct solution for z (=D/C) for these rows. However, you have a range of values from 6.4 to 10.11, so there is no exact solution for the value of z.

Hope this helps.

Pete