The solution to a system of two linear equations is x = 3 weeks; y = 9 feet
Match the description with the correct statement.
How could you get exactly two or three solutions to this linear system?
Match the description with the correct statement:
Exactly two solutions:
- Add a third equation that is a linear combination of the original two equations.
Exactly three solutions:
- Create a dependent system by multiplying one of the equations by a constant and adding them together.
- Create a dependent system by multiplying both equations by different constants and adding them together.
To get exactly two or three solutions to a system of linear equations, there are a few possibilities:
1) Graphical Method: Plot the two linear equations on a coordinate plane and determine the points of intersection. If there are exactly two points of intersection, this corresponds to two solutions. If there are exactly three points of intersection, this corresponds to three solutions.
2) Algebraic Method: Use substitution or elimination to solve the system of linear equations. If, after solving the equations, you end up with two or three distinct sets of values for x and y that satisfy both equations, then you have two or three solutions.
In the given case, where the solution is x = 3 weeks and y = 9 feet, we have a single solution rather than two or three solutions.
To get exactly two solutions to a linear system, the equations must represent two intersecting lines. The lines must have different slopes and different y-intercepts.
To get exactly three solutions to a linear system, the equations must represent two coinciding lines, meaning they are the same line. The equations must have the same slope and the same y-intercept.