Look at the system of equations below.
4x-5y=3
3x+5y=13
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. The elimination method is indeed the best method for solving this system because the y-coefficients in the two equations are opposites of each other.
When using the substitution method, we would need to solve one equation for one variable and substitute it in the other equation. In this case, if we solve the first equation for x or y, we would still end up with a variable coefficient in the second equation that is not the opposite of the corresponding variable coefficient in the first equation. This would make the substitution method more complicated and time-consuming compared to using the elimination method.
Graphing could also be an option, but it is not as efficient as elimination in this case. Graphing involves plotting the two equations on a coordinate plane and finding the point of intersection, which is the solution to the system. However, the point of intersection might not be precise, and it can be challenging to determine its exact coordinates on the graph. Additionally, graphing requires more time and effort compared to the elimination method, making it a less efficient choice.