Systems of Equations with Three Variables

Given
Π0 = 0.5Π0 + 0.3Π1 +0.2 Π2
Π1 = 0.4Π0 + 0.4Π1 + 0.3Π2
Π2 = 0.1Π0 + 0.3Π1 + 0.5Π2

Where 1 = Π0 + Π1 + Π2

The solution should yield:
Π0 = 21/62
Π1 = 23/62
Π2 = 18/62

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-0.1Π0 - 0.3Π1 + 0.5Π2 = 0----------------(iii)
Where 1 = Π0 + Π1 + Π2
Subtract (iii) from (i), we will get
0.6Π0 - 0.7 Π2 = 0
Multiply equation (iii) by 2 and add it to (ii)
-0.6Π0 + 0.7Π2= 0
These two equations are the same.
Now, -0.6 Π0 = -0.7Π2
 Π0 = 7/6 Π2
Substitute this in 1 = Π0 + Π1 + Π2 , we will get
7/6 Π2 + Π1 + Π2= ...