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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) 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? The solution to this system could possibly have this meaning. :: From the origin, find the y-intercepts and subtract them The point where the 9 foot plant stopped growing for 3 weeks :: Find the point where the two lines cross; (3,9) : The point showing after 3 weeks, the plant was 9 feet tall : Curving the lines around so that they cross multiple times : No way to have 2 linear graphs with 2 or 3 intersecting points :: Making the lines parallel to each other :: The point where the lines cross the y-axis after 3 weeks
How could you get exactly two or three solutions to this linear system? - Curving the lines around so that they cross multiple times
How would you locate the solution of the two linear graphs on the coordinate plane? The solution to this system could possibly have this meaning. - Find the point where the two lines cross; (3,9)
The point where the 9 foot plant stopped growing for 3 weeks - The point showing after 3 weeks, the plant was 9 feet tall
From the origin, find the y-intercepts and subtract them - No way to have 2 linear graphs with 2 or 3 intersecting points
Making the lines parallel to each other - The point where the lines cross the y-axis after 3 weeks
To get exactly two or three solutions to this linear system, you could curve the lines around so that they cross multiple times. This allows for the possibility of more than one intersection point.
To locate the solution of the two linear graphs on the coordinate plane, you would need to find the point where the two lines cross. In this case, the solution is given as (3,9), which means that after 3 weeks, the plant was 9 feet tall.
The point showing where the 9 foot plant stopped growing for 3 weeks is not the correct answer because it refers to the y-intercept, which may not necessarily represent the solution.
Making the lines parallel to each other would not allow for any intersections, so it does not result in two or three solutions.
The point where the lines cross the y-axis after 3 weeks is not the correct answer either, as it refers to the y-intercept and does not directly provide information about the solution.
In summary, the correct statements are:
1. How could you get exactly two or three solutions to this linear system? : Curving the lines around so that they cross multiple times
2. How would you locate the solution of the two linear graphs on the coordinate plane? : Find the point where the two lines cross; (3,9) : The point showing after 3 weeks, the plant was 9 feet tall
To get exactly two or three solutions to a linear system, there are a few possibilities. One way is if the two lines representing the equations in the system intersect at two distinct points or coincide with each other. Another way is if the two lines are parallel and coincide with each other. In these cases, you would have either two or three solutions respectively.
To locate the solution of the two linear graphs on the coordinate plane, you would need to find the point where the two lines intersect. This point represents the values of x and y that satisfy both equations in the system. In this case, the point where the two lines intersect is (3,9), which means that after 3 weeks, the plant was 9 feet tall.
From the given descriptions, the one that matches finding the point where the two lines cross, (3,9), is: The point showing after 3 weeks, the plant was 9 feet tall.
The description "From the origin, find the y-intercepts and subtract them" is not accurate because the y-intercepts are not relevant for finding the solution of the system.
The description "The point where the 9-foot plant stopped growing for 3 weeks" is also not accurate. The solution of the system represents the point where the two lines intersect, not where the plant stopped growing.
The descriptions "Curving the lines around so that they cross multiple times" and "Making the lines parallel to each other" are not correct, as they do not lead to a linear system with two or three solutions.
Finally, "The point where the lines cross the y-axis after 3 weeks" does not describe the solution in this case because the point (3,9) represents where the lines cross after 3 weeks, not specifically on the y-axis.