Use the method of elimination to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form.
\[
\left\{\begin{array}{r}
2 x+2 y=-2 \\
10 x+10 y=-10
\end{array}\right.
\]

Answer
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Only One Solution
Inconsistent System
Dependent System
$\{c$
)

Step 1 ：The system of equations given is: \[ \left\{\begin{array}{r} 2 x+2 y=-2 \ 10 x+10 y=-10 \end{array}\right. \]

Step 2 ：The method of elimination involves adding or subtracting the equations in order to eliminate one of the variables, making it possible to solve for the other variable. However, in this case, it is clear that both equations are multiples of each other. This means that they are not independent and the system of equations is dependent.

Step 3 ：In a dependent system, there are infinitely many solutions and the solution set can be expressed in terms of one of the variables.

Step 4 ：To express the solution set in terms of one of the variables, we can solve one of the equations for one variable in terms of the other. Let's solve the first equation for x in terms of y.

Step 5 ：The solution to the equation is \(x = -y - 1\). This means that for any value of y, x will be equal to -y - 1. This is the solution set for the dependent system of equations.

Step 6 ：Final Answer: The solution set for the dependent system of equations is \(\boxed{x = -y - 1}\).