how to solve system of eqns ?

Question

A+B+C=195 ................(1)
B+C+D=210.................(2)
C+D+E=196.................(3)
D+E+F=208.................(4)
E+F+G=213.................(5)
A+B+C+D+E+F+G=491....(6)


whats the value of G,A,D ?

Soln given :G=88 , A=68,D=83


How to solve this eqn ?

can anybody please give me some hints which equations to take and solve to find G,A,D ?


please dont provide soln but give hints.

thanks

Answer 1

First,
Look at (1) and (4), then plug into 6
a + b+ c + d + e + f + g = 491,
a + b + c = 195 and d + e + f =208
195 + 208 + g = 491
or g = 88
Look at (5)
e + f + g =213 or
e + f + 88 = 213
e + f = 125
Now look at (4)
d + e + f = 208, but e + f = 125
d + 125 = 208
d = 83
Now look at (2)
b + c + d = 210
b + c + 83 = 210
b + c =127
Now look at 1
a + b + c = 195
a + 127 = 195
a = 68

Answer 2

You have six equations in seven unknowns. Therefore, one of the unknowns must be a parameter with some or all of the other unknowns expressed in terms of this parameter.

By reducing the augmented matrix to its reduced row echelon form, you will find that A = 68, B = 14, C = F + 12, D = 83, E = 125 - F, and G = 88. F may be given any value. You were only asked to find G, A, and D because those do not depend on F.