Look at the system of equations below. A student makes this argument: Elimination is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation. Complete the student’s argument by explaining why substitution and graphing are less efficient methods than elimination for this system. (4 points)
The student's argument is not valid. While it is true that the y-coefficients in the two equations are opposites of each other, this alone does not make elimination the best method for solving the system.
Substitution involves solving one equation for one variable, and then substituting that expression into the other equation. This method can be less efficient when dealing with complex expressions or equations that are not easily solvable for one variable.
Graphing involves plotting the equations on a coordinate plane and finding the intersection point(s) of the two graphs. This method can be less efficient when dealing with equations that do not have easily distinguishable intersection points or when the intersection point(s) have decimal or irrational coordinates.
On the other hand, elimination involves adding or subtracting the equations in order to eliminate one variable, resulting in a simpler equation that can be solved for the remaining variable. This method can be more efficient when dealing with equations that have easily eliminated variables or when the resulting equation is solvable by simplest methods.
Therefore, in this specific system, elimination may be the most efficient method due to the easily eliminated y-variables, but the student's argument is not valid as it does not consider the specific characteristics of substitution and graphing methods.