The solution to a system of two linear equations is x = 3 weeks: y = 9 feet
Match the description with the correct statement.
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.
How could you get exactly two or three solutions to this linear system?
To locate the solution of the two linear graphs on the coordinate plane, you would plot the two equations on the same set of axes and find the point where the two lines intersect.
The statement "The solution to this system could possibly have this meaning" does not provide enough information to determine a specific option.
To get exactly two or three solutions to this linear system, the two equations would have to be parallel lines or coincide with each other.
1. How would you locate the solution of the two linear graphs on the coordinate plane?
- Plot the two linear equations on the same coordinate plane.
- Look for the point of intersection of the two lines.
- The coordinates of the point of intersection represent the solution to the system.
2. The solution to this system could possibly have this meaning.
- The value of x represents the number of weeks, and the value of y represents the number of feet in the given context.
- Therefore, the solution x = 3 weeks, y = 9 feet represents a specific time period and distance in the context of the problem.
3. How could you get exactly two or three solutions to this linear system?
- By graphing the equations, examine the number of points of intersection.
- If there are two distinct points of intersection, then the system has exactly two solutions.
- If the lines are overlapping, resulting in infinite points of intersection, then the system has infinitely many solutions.
- If the lines are parallel and do not intersect, then the system has no solutions.
To locate the solution of the two linear graphs on the coordinate plane, you would need to plot the equations as lines and find the point of intersection between the two lines. This point represents the solution to the system of equations.
The correct statement that matches the description would be: "How would you locate the solution of the two linear graphs on the coordinate plane?"
The meaning of the solution "x = 3 weeks, y = 9 feet" could possibly be that it represents a point in a real-world scenario where x represents the time in weeks and y represents the distance in feet. Without more context, it is difficult to determine the exact meaning of the solution.
The correct statement that matches the meaning of the solution would be: "The solution to this system could possibly have this meaning."
To get exactly two or three solutions to a linear system, the system would need to have specific characteristics. One possible way would be when the two lines representing the equations are parallel, resulting in no intersection point and no solution. Another way would be when the two lines overlap each other, resulting in infinitely many solutions as every point on the overlapping section satisfies both equations.
The correct statement that matches how to get exactly two or three solutions to this linear system would be: "How could you get exactly two or three solutions to this linear system?"