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What are the intersection points of the parabola given by the equation y = x -9 and the line given by the equation y = x - 3?

A. (-3,-6) and (2, -1)
B. (-3,0) and (4,7)
C. (3,0) and (-2,-5)
D. (3,0) and (-4, -7)

User Lingceng
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1 Answer

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Final answer:

The question likely contains an error because the two equations y = x - 9 and y = x - 3 have the same slope but different y-intercepts, indicating they are parallel and do not intersect. Therefore, none of the given answers with intersection points would be correct.

Step-by-step explanation:

To find the intersection points of the parabola y = x - 9 and the line y = x - 3, we need to set the equations equal to each other because at the intersection points, the y-values (and x-values) of the parabola and the line are the same. Solving the equation x - 9 = x - 3 gives us no solution since the x terms cancel out, and we are left with -9 ≠ -3, which is a contradiction. This suggests that there was an error in the question, as these two equations represent the same slope and there cannot be distinct intersection points; rather, if the lines were parallel with different constants, they would never intersect, and if the constants were the same, they would be the same line.

User Xis
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