   SEARCH HOME Math Central Quandaries & Queries  Question from Sean, a student: this is a linear equations problem; my teacher gave me the solution worked out but I am not sure how she solved it exactly first: 3535.5 + Fbd (.866) + Fbc (.5) - Fab (.5) = 0 and -3535.5 - Fab (.866) - Fbc (.5) - Fbd (.5) = 0 next: 3535.5 + Fbd (.866) - Fab (.5) = 0 3535.5 - Fbd (.5) - Fab (.866) = 0 -6123.5 - Fbd (1.5) + Fab (.866) = 0 -9659 = Fbd 2.0 and the answers are: Fbd = -4829.5 Fab = - 1293.7 could you please tell me how to solve this in the traditional linear systems method Sean,

You are given the equations

3535.5 + Fbd (.866) + Fbc (.5) - Fab (.5) = 0
-3535.5 - Fab (.866) - Fbc (.5) - Fbd (.5) = 0

Since you have more unknowns than equations you are not going t obtain a unique solution.

My first action was to rearrange the two equations to obtain

3535.5 - Fab(.5) + Fbc (.5) + Fbd (.866) = 0
-3535.5 - Fab (.866) - Fbc (.5) - Fbd (.5) = 0

and then add the equations to get

-Fab(1.366) + Fbd(.366) = 0

or

Fbd = Fab(0.3732)

If you substitute this back into the two given equations they both simplify to the same equation

3535.5 + Fab(2.732) + Fbc(0.5) = 0

or

Fbc = -7071 - Fab(5.464)

Hence you can give Fab any value and obtain a solution with that value for Fab and Fbd and Fbc determined by the highlighted equations.

Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.