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Match the correct solution to each system of equations graphed below. *Not all answers will be used. Place the correct solution beneath the graph it matches to.(4 points)

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

(0, -1)
infinitely many solutions
( -1.5, 4.5 )
no solutions
(1,1)
(-1,2)

1 answer

To match the solutions to the systems of equations graphed, you'll need to analyze the graphs carefully. Here’s a guide to interpreting the solutions:

  1. (0, -1): This would be a point where two lines intersect, suggesting a unique solution.

  2. Infinitely many solutions: This occurs when two lines overlap completely, leading to an infinite number of intersection points.

  3. (-1.5, 4.5): This is another unique point of intersection between two lines.

  4. No solutions: This is the case when two lines are parallel and never intersect.

  5. (1,1): Another point of intersection, which would indicate a unique solution for that system.

  6. (-1, 2): This would also represent a unique intersection.

To provide the correct responses beneath each graph, you would need to observe the solutions of each system based on the graphs.

For each graph, determine whether there’s an intersection point, whether the lines are parallel, or if they are overlapping.

Once you assess the graphs, you can place the appropriate responses below each one as follows:

  • For a graph showing two lines that intersect at (0, -1), you'd write (0, -1) below it.
  • If a graph shows two lines that are the same, write "infinitely many solutions."
  • For lines that do not cross, write "no solutions."
  • For any unique points like (1,1) or (-1.5, 4.5), place those as their respective matches.

Without seeing the actual graphs, I cannot definitively place the solutions, but that's how you should approach matching them!