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9x + 2y = 0

3x - 5y = 17

Multiply the second equation by -3 so now the system looks like:

9x + 2y = 0

-9x + 15y = -51

So now when we add the two equations together (in their like-terms columns), we are left with just one variable:

0x + 17y = -51

Solve for y:

17y = -51

y = -3

And plug y = -3 into either of the original equations to get the value of x:

9x + 2y = 0

9x + 2(-3) = 0

9x - 6 = 0

9x = 6

x = 2/3

So the answer is x = 2/3 and y = -3.

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