The solution to a system of two linear equations is x = 3 weeks; y = 9 feet
Match the description with the correct statement.
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?
How could you get exactly two or three solutions to this linear system?
Description: The number of weeks is directly proportional to the number of feet.
Statement: The solution represents the relationship between the number of weeks and the number of feet, where for every 1 week, there are 3 feet.
To locate the solution of the two linear graphs on the coordinate plane, you would plot the point (3, 9) which represents x = 3 weeks and y = 9 feet.
To get exactly two or three solutions to this linear system, you could add or subtract multiples of the equations or change the coefficients of the equations to create new lines that intersect at different points.
Match the description with the correct statement:
The solution to this system could possibly have this meaning: "x represents the number of weeks, and y represents the number of feet."
To locate the solution of the two linear graphs on the coordinate plane, you would need to plot the graphs of the two linear equations and find the point where they intersect. This point represents the solution to the system.
To get exactly two or three solutions to this linear system, you would need to have either two parallel lines (no intersection) or two identical lines (infinite intersections).
Match the description with the correct statement:
- The solution to this system could possibly have this meaning: None of the given options are suitable to match with this description.
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 need to graph the two linear equations and find the point of intersection. The coordinates of this point represent the solution to the system of equations.
How could you get exactly two or three solutions to this linear system?:
- A system of linear equations can have exactly two or three solutions if the lines of the equations intersect at different points. This can occur if the equations represent parallel lines or if they represent a line and a coincident line (overlapping each other). In these cases, the system can have infinite solutions (such as in the case of coincident lines) or no solution (in the case of parallel lines).