Problem

Line $1: y=\frac{1}{2} x-\frac{9}{2}$

Line 2: $y=-x$

This system of equations is:
inconsistent
consistent dependent
consistent independent

This means the system has:
a un yue solution
Solution: (I]. [D)
infinitely many solutions no solution

Answer

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Answer

Final Answer: The system of equations is \(\boxed{\text{consistent independent}}\) and it has \(\boxed{\text{a unique solution}}\).

Steps

Step 1 :Given the two equations: Line 1: \(y=\frac{1}{2} x-\frac{9}{2}\) and Line 2: \(y=-x\)

Step 2 :To determine the nature of the system of equations, we need to find the intersection point of the two lines.

Step 3 :We can find the intersection point by setting the two equations equal to each other and solving for x. Then we can substitute x into one of the equations to find y.

Step 4 :Upon solving, we get the solution as \(x = 3.00000000000000\) and \(y = -3.00000000000000\)

Step 5 :The solution to the system of equations is a valid pair of (x, y), which means the two lines intersect at a single point.

Step 6 :Therefore, the system is consistent independent. This means the system has a unique solution.

Step 7 :Final Answer: The system of equations is \(\boxed{\text{consistent independent}}\) and it has \(\boxed{\text{a unique solution}}\).

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