Question

Question

The solution to a system of two linear equations is x = 3 weeks; y = 9 feet

Match the description with the correct statement.

(3 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.
How could you get exactly two or three solutions to this linear system?
The solution to this system could possibly have this meaning.
How would you locate the solution of the two linear graphs on the coordinate plane?
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Answer 1

To match the descriptions with the correct statements, here are the possible responses that you can use:

1. How could you get exactly two or three solutions to this linear system?

   • For a linear system to have an infinite number of solutions, the equations must represent the same line, which occurs when they are dependent. For exactly two distinct solutions, the equations must intersect at two points, which is not possible for linear equations in a two-dimensional space since they can either be parallel (no solutions) or intersect at only one point (one solution). Therefore, this response is not applicable.

2. The solution to this system could possibly have this meaning.

   • The solution to the system (x = 3 weeks; y = 9 feet) means that at 3 weeks, the quantity being measured is 9 feet.

3. How would you locate the solution of the two linear graphs on the coordinate plane?

   • To locate the solution of the two linear graphs on the coordinate plane, you would plot both equations on the graph. The point where the two lines intersect represents the solution to the system of equations.

You can insert these responses into the appropriate input fields as per their descriptions.