Suppose that $-x+y=9$ and $2x+3y=17$. What is $y?$
$$y=$$

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 $y=\boxed{{\displaystyle 7}}$.