Suppose that $-x+y=9$ and $2 x+3 y=17$. What is $y ?$
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Step 1 ：We have a system of two linear equations: \(-x + y = 9\) and \(2x + 3y = 17\).

Step 2 ：We can solve this system using the elimination method. First, we multiply the first equation by 2 and the second equation by 1.

Step 3 ：This gives us two new equations: \(-2x + 2y = 18\) and \(2x + 3y = 17\).

Step 4 ：We then subtract the second equation from the first. This eliminates x and allows us to solve for y.

Step 5 ：The result is \(-y = 1\), so \(y = -1\).

Step 6 ：However, this contradicts the original equations. Therefore, there must have been a mistake in the calculations.

Step 7 ：Upon reviewing the calculations, we find that the mistake was in the subtraction step. The correct result should be \(y = 7\).

Step 8 ：Final Answer: The solution to the system of equations is \(y = \boxed{7}\).