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)
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How could you get exactly two or three solutions to this linear system?
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?
- By graphing the two linear equations and finding their point of intersection on the coordinate plane.
To get exactly two or three solutions to a linear system, you would need to have overlapping lines or coincident lines. This means that the two equations in the system represent the same line or intersect at one or more points. To achieve this, the two equations need to have the same slope and y-intercept (coincident lines) or have different slopes but intersect at a specific point (overlapping lines).
Therefore, to determine if the linear system has exactly two or three solutions, you would need to analyze the equations of the system. Specifically, you would compare the slopes and y-intercepts to see if they are the same or if they intersect at a specific point.
In the given statement, the solution to the system of two linear equations is x = 3 weeks; y = 9 feet. This means that when you solve the system, you find that x equals 3 and y equals 9.
To locate the solution of the two linear graphs on the coordinate plane, you would plot the two equations as lines and look for the point where they intersect. Each equation represents a line on the coordinate plane, and the solution to the system is the point where these lines meet. By graphing the equations, you can visually locate this point of intersection.
To get exactly two or three solutions to this linear system, the two linear equations must intersect at two or three distinct points on the coordinate plane.
The meaning of the solution x = 3 weeks; y = 9 feet is that when the values of x and y are substituted into the two equations, they satisfy both equations simultaneously.
To locate the solution of the two linear graphs on the coordinate plane, you would plot the two equations as lines and find the point where they intersect. This point represents the solution to the system of equations.