Example 2 - Solve 2x2 Systems of Equations using Gauss Elimination

Example:
Solve w/ Gauss Elimination 2x2 system
   x + 2 y = 4
-2 x + 6 y = 2

Solution:
make a₁₁ = 1
    x + 2 y = 4   <---- (row 1) /1
-2 x + 6 y = 2

make a₂₁ = 0
 1 x + 2 y = 4  
-2 x + 6 y = 2 <---- (row 2) + 2 (row 1) or (row 2) - (-2) (row 1)

make a₂₂ = 1
1 x + 2   y = 4  
0 x + 10 y = 10  <---- (row 2) / 10

Now in Gauss Form
row 1:  1 x + 2 y = 4  
row 2:  0 x + 1 y = 1
"zeros" below the diagonal and "ones" in the diagonal

... from row (2): 1 y = 1 or y = 1
... from row (1): x = 4 - 2 y ;  x = 2
the solution is: (2 , 1)