First, get rid of fractions:

2x/3 - y = 2 x + y/2 = 1

3     2

2x - 3y = 6 2x + y = 2

Next, multiply the second equation by (-1) to eliminate x:

2x - 3y = 6 2x + y = 2

(-1)

2x - 3y = 6 -2x - y = -2

Adding gives -4y = 4, so that y = -1. Substituting this result into the first equation gives x = 3/2.

Thus, the (unique) solution is (3/2, -1).

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