Multiply all terms in the first equation by 2 and all terms in the second by 3.
You should obtain:
6x + 16y = 34
-6x + 27y = 9
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43y =43, and so y = 1. Subbing 1 for y in the first eq'n, we get
3x + 8(1) = 17, or 3x = 9, or x = 3.
The solution is (3, 1).