The problem asks us to find the value of $x$ such that the lines $2x+2$ and $x+56$ are parallel and to find the value of $y$ such that the lines $y+7$ and $3y-17$ are parallel. Since the lines are given as horizontal lines, two lines are parallel if and only if their equations are of the form $y=c_1$ and $y=c_2$, where $c_1$ and $c_2$ are constants. For two lines to be parallel we need $c_1 \ne c_2$.

1. Problem Description

The problem asks us to find the value of $x$ such that the lines $2x+2$ and $x+56$ are parallel and to find the value of $y$ such that the lines $y+7$ and $3y-17$ are parallel. Since the lines are given as horizontal lines, two lines are parallel if and only if their equations are of the form $y=c_1$ and $y=c_2$, where $c_1$ and $c_2$ are constants. For two lines to be parallel we need $c_1 \ne c_2$.

2. Solution Steps

First, we find the value of $x$ so that the first two lines are parallel. For the lines $2x+2$ and $x+56$ to be parallel, their corresponding $y$ values must be different. However, since the question does not indicate lines must be parallel, let's find $x$ such that the lines are the same line, then simply require that we not choose that value.

If we set $2x+2 = x+56$, we get $2x - x = 56 - 2$, which gives $x = 54$. Then we need $x \ne 54$.

Next, we find the value of $y$ so that the lines $y+7$ and $3y-17$ are parallel.

For the lines $y+7$ and $3y-17$ to be parallel, we need to have $y+7 \ne 3y-17$.

If we set $y+7 = 3y-17$, we get $2y = 24$, so $y = 12$.

Then we need $y \ne 12$.

3. Final Answer

$x$ can be any value except $54$. $y$ can be any value except $12$.

Final Answer: $x \ne 54$ and $y \ne 12$.

However, if the problem requires the lines to be equal instead of parallel, then $x=54$ and $y=12$.

Since the problem asks for the lines to be parallel, this means the value of $x$ is any value not equal to $54$, and the value of $y$ is any value not equal to $12$.

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