Match them up
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? Find the point where the two lines cross; (3,9)
- The solution to this system could possibly have this meaning: The point showing after 3 weeks, the plant was 9 feet tall.
- How could you get exactly two or three solutions to this linear system?
Answer: 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?
Answer: Find the point where the two lines cross; (3,9)
- The solution to this system could possibly have this meaning.
Answer: The point showing after 3 weeks, the plant was 9 feet tall
- The point where the 9 foot plant stopped growing for 3 weeks
Answer: The point where the lines cross the y-axis after 3 weeks
- The point where the lines cross the y-axis after 3 weeks
Answer: From the origin, find the y-intercepts and subtract them
- No way to have 2 linear graphs with 2 or 3 intersecting points
Answer: Making the lines parallel to each other
The correct match for each description is as follows:
- 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? :: Find the point where the two lines cross; (3,9)
- The solution to this system could possibly have this meaning. :: The point showing after 3 weeks, the plant was 9 feet tall
- 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
To get exactly two or three solutions to a linear system, the lines representing the equations need to intersect at two or three distinct points. This can be achieved by curving the lines around so that they cross multiple times.
To locate the solution of the two linear graphs on the coordinate plane, you need to find the point where the two lines intersect. In this case, the solution is given as (3,9), indicating that after 3 weeks, the plant was 9 feet tall.
The point where the 9-foot plant stopped growing for 3 weeks refers to the point where the lines cross the y-axis after 3 weeks. That's because the y-intercept represents the value of y when x is equal to 0.
It's not possible to have two linear graphs with exactly 2 or 3 intersecting points if the lines are parallel to each other. Parallel lines do not intersect, so they cannot have more than one point in common.
Therefore, the correct match for the statement is:
- Making the lines parallel to each other.