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

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 \(\boxed{\text{a unique solution}}\).