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System of Equations (how do I solve it)

Mathematics
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Dec 12th, 2014

Pi1=0.4Pi1+0.45Pi2+0.8Pi3 ===> 0.6Pi1=0.45Pi2+0.8Pi3   (1)

Pi2=0.35Pi1+0.4Pi2+0.15Pi3 ===>  0.6Pi2=0.35Pi1+0.15Pi3  (2)

Pi3=0.25Pi1+0.15Pi2+0.05Pi3 ===> 0.95Pi3=0.25Pi1+0.15Pi2   (3)

From Equation 1  we have Pi1=0.75Pi2+1.33Pi3

So Equation 2 could be written as 

0.6Pi2=0.35(0.75Pi2+1.33Pi3)+0.15Pi3

0.6Pi2-0.35x0.75Pi2=0.35x1.33Pi3+0.15Pi3

0.3375Pi2=0.6155Pi3

Pi2=1.824Pi3

So Pi1=0.75Pi2+1.33Pi3=0.75x1.824Pi3+1.33Pi3=2.698Pi3

Therefore, Pi1+Pi2+Pi3=2.698Pi3+1.824Pi3+Pi3=1

5.522Pi3=1

Pi3=1/5.522=0.18

Pi2=1.824Pi3=1.824x0.18=0.33

Pi1=2.698Pi3=2.698x0.18=0.49

Dec 12th, 2014

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