Question

in analyzing the forces A,B,C and D the following equations are used. find these forces?
A+B=850
A+B+400=0.8C+0.6D
0.6C=0.8D
5A-5B+4C-3D=0

Answer 1

IS it not solving simple equations with variables.

A+B = 850        substitute this in the second equation
850 + 400 = 0.8C + 0.6 D

0.8 C + 0.6 D = 1250  multiply by 5

4 C + 3 D = 6250  --- equation 5

Given 0.6 C = 0.8 D    (3rd equation)       so  C = 0.8/0.6 D = 4/3 D
substitute in the 5th equation: 
4 * 4/3 D + 3 D = 6250      so  (16/3+3) D  = 6250
D = 6250 * 3 / 25 = 750

C = 4/3 * 750 = 1000

substitute these in the last equation
5A - 5B + 4000 - 3*750 = 0    => 5(A-B) = - 1750
So A - B = - 350  -- equation 6
Combine with equation 1  :  A+B = 850

Add equ 6 and equ 1      =>  2 A = 500    A = 250
B = 850 - 250 = 600