Problem

Line 1: $y=-x-2$

Line $2: y=-\frac{1}{2} x-2$

This system of equations is:
inconsistent
consistent dependent
consistent independent

Answer

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Answer

Final Answer: The system of equations is \(\boxed{\text{consistent independent}}\).

Steps

Step 1 :The given system of equations is: Line 1: \(y=-x-2\) and Line 2: \(y=-\frac{1}{2} x-2\).

Step 2 :A system of equations is consistent if there is at least one set of values for the variables that satisfies all the equations in the system. It is inconsistent if there is no set of values that satisfies all the equations.

Step 3 :A system of equations is dependent if every solution of one equation is also a solution of the other equations. It is independent if there is at least one solution that is not a solution of any other equation.

Step 4 :In this case, we can see that the two lines have different slopes (-1 and -1/2), which means they are not parallel and will intersect at some point. Therefore, the system is consistent.

Step 5 :However, since the two lines are not the same, there is not an infinite number of solutions, which means the system is independent.

Step 6 :So, the system of equations is consistent and independent.

Step 7 :Final Answer: The system of equations is \(\boxed{\text{consistent independent}}\).

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