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.
The student's argument is valid because elimination is the most efficient method for solving the system of equations when the coefficients of either x or y are opposites.
Substitution method involves solving one equation for one variable and substituting it into the other equation. In this case, substituting would result in a more complicated equation with a higher degree or additional terms, making the process more time-consuming.
Graphing method is less efficient because it relies on visualizing and interpreting the intersection point of the two equations on a graph. This can be inaccurate or imprecise, especially when the intersection point is not a whole number or when dealing with complex or fractional coefficients.
On the other hand, the elimination method simplifies the system by adding or subtracting the equations to eliminate one variable. In this case, since the y-coefficients are opposites, adding the equations will eliminate the y variable, making it easier to solve for x.