(poor method for this particular question, but ...)
solve the second for x, (I look for the smallest coefficient)
3x = 5+8y
x = (5+8y)/3
sub into the first
5(5+8y)/3 - 9y = 17
multiply by 3 to eliminate fractions
5(5+8y) - 27y = 51
25 + 40y - 27y = 51
13y = 26
y = 2
then x = (5+16)/3 = 7
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