Example 1 - Solve 2x2 Systems of Equations using Gauss Elimination

Example:
Gauss Elimination 2x2 system
2 x + 4 y = 16
3 x + 5 y = 22

Solution:
make a₁₁ = 1
row 1 -->   2 x + 4 y = 16   <---- (row 1) /2
row 2  -->  3 x + 5 y = 22

make a₂₁ = 0
1 x + 2 y = 8  
3 x + 5 y = 22  <---- (row 2) - 3 (row 1)
(ie. eliminate "x" in 2nd row, 3rd row etc... by adding / subtracting multiples of row1.)

make a₂₂ = 1
1 x + 2 y = 8
0 x - 1 y = -2 <---- (row 2) / -1

Now in Gauss Form
1 x + 2 y = 8
0 x + 1 y = 2
"zeros" below the diagonal and "ones" in the diagonal

From (2): 1 y = 2 or y = 2
back sub. in (1): ... x = 4
 the solution is (4 , 2)