manipulate the equations so that all elements below the main diagonal are zero.
So, subtract row 1 from 2/3 of row 2:
2x + y = 3
2x - 4/3 y = 2/3
2x + y = 1
-7/3 y = -7/3
y = 1
now plug that into row 1 to get x = 1
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