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

Answer 1

Let's break down the questions and match them with the appropriate statements:

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

   • The solution \(x = 3\) weeks and \(y = 9\) feet means that at 3 weeks, the two linear equations intersect at a point where the corresponding values of \(x\) and \(y\) are 3 weeks and 9 feet, respectively. This could represent a specific scenario, such as the time it takes to reach a certain distance or height, depending on the context of the equations.

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

   • In a linear system of two equations in two variables, there can be exactly one solution (intersection point), infinitely many solutions (the same line), or no solution (parallel lines). To get exactly two or three solutions, you would typically require a different type of system, such as a nonlinear system (e.g., a linear equation paired with a quadratic equation) or by changing the coefficients in such a way that the new system has multiple points of intersection.

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 graph both equations on the same set of axes. The point where the two lines intersect represents the solution to the system. In this case, you would plot the point (3, 9) on the graph, which indicates that at 3 weeks (x-axis), the value of the other variable is 9 feet (y-axis).

In summary, the three responses would be:

1. The meanings imply specific contexts or scenarios based on the equations.
2. You would require a different type of system for multiple solutions.
3. You locate the solution by plotting both equations and finding their intersection on the graph.

Answer 2

answers: :: Curving the lines around so that they cross multiple times
:: From the origin, find the y-intercepts and subtract them
:: The point where the 9 foot plant stopped growing for 3 weeks
:: The point where the lines cross the y-axis after 3 weeks
:: No way to have 2 linear graphs with 2 or 3 intersecting points
Making the lines parallel to each other
:: Find the point where the two lines cross; (3, 9)