You can
put this solution on YOUR website! .7a + .25b + .3c = a
.2a + .6b + .05c = b
.1a + .15b + .65c = c
WHERE a + b + c = 1
1st equation: .7a + .25b + .3c = a
2nd equation: .2a + .6b + .05c = b
3rd equation .1a + .15b + .65c = c
4th equation a + b + c = 1
Subtract a, b, and c from both sides of the first three
equations, respectively, and you have this system:
-.3a + .25b + .3c = 0
.2a - .4b + .05c = 0
.1a + .15b - .35c = 0
a + b + c = 0
The augmented matrix of this system is
[-.3 .25 .3 | 0]
[ .2 -.4 .05 | 0]
[ .1 .15 -.35 | 0]
[ 1 1 1 | 1]
which is row equivalent to its row reduced echelon form:
[1 0 0 53/111]
[0 1 0 10/37]
[0 0 1 28/111]
[0 0 0 0 ]
a = 53/111
b = 10/37
c = 28/111
Edwin
AnlytcPhil@aol.com
