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? Answer:
How could you get exactly two or three solutions to this linear system? Answer:
The solution to this system could possibly have this meaning. Answer:
- How would you locate the solution of the two linear graphs on the coordinate plane? Answer: By finding the point where the two lines intersect.
- How could you get exactly two or three solutions to this linear system? Answer: By having overlapping or coinciding lines.
- The solution to this system could possibly have this meaning. Answer: The x-coordinate represents the number of weeks and the y-coordinate represents the length in feet.
How would you locate the solution of the two linear graphs on the coordinate plane? Answer: To locate the solution of the two linear graphs on the coordinate plane, you would plot the two linear equations as lines on the coordinate plane, and the point of intersection of these lines represents the solution to the system of equations.
How could you get exactly two or three solutions to this linear system? Answer: In a system of two linear equations, you can get exactly two solutions if the lines representing the equations intersect at two distinct points. You can get exactly three solutions if the lines representing the equations coincide with each other, meaning they are the same line.
The solution to this system could possibly have this meaning. Answer: The solution to the system of equations represents the point at which the two lines intersect, which in the given context, would mean that x=3 weeks and y=9 feet.
How would you locate the solution of the two linear graphs on the coordinate plane? Answer: To locate the solution of two linear equations on the coordinate plane, you can graph both equations and find the point where they intersect. The point of intersection represents the solution to the system of equations.
How could you get exactly two or three solutions to this linear system? Answer: For a linear system to have exactly two or three solutions, the two equations must represent two parallel lines that intersect with a third line at two points or coincide with the third line entirely. In other words, the system of equations must have either infinitely many solutions (the lines coincide) or no solutions (the lines are parallel).
The solution to this system could possibly have this meaning. Answer: The solution to a linear system of equations represents the values of the variables (x and y) that satisfy both equations simultaneously. In the given example, the solution x=3 weeks and y=9 feet means that at the point of intersection, the x-coordinate corresponds to a time of 3 weeks and the y-coordinate corresponds to a measurement of 9 feet.