Solving Systems of Nonlinear Multivariate Equations

**Background:** I am working on a project involving blending metallurgical coals, and developing a blending model involves repeatedly solving systems of nonlinear multivariate equations.

**What I Need: **I need a means (either an excel or other program) that will enable me to repeatedly (and efficiently) solve systems of equations like the following:

(1) (19.4/0.62) = (1.5/a) + (44.1/b) + (27.6/c) + (1.5/d)

(2) (18.0/0.57) = (1.5/a) + (38.1/b) + (29.7/c) + (6.9/d)

(3) (15.7/0.48) = (1.5/a) + (38.0/b) + (38.0/c) + (0.8/d)

(4) (16.8/0.61) = (0/a) + (3.1/b) + (42.9/c) + (32.0/d)

Solving for the values of a, b, c & d (which are constants)

**Note: **The numbers in the equations have been rounded to one or two decimal places. I am not sure if this will be an issue when trying to solve for the four constants.

Thanks in advance for your help!