Give an example of a system that would be best solved with elimination.
Solving a system of linear equations with multiple variables is a common situation where elimination would be the best method. For example, consider the system of equations:
2x + 3y = 8
4x - y = 11
By using the elimination method, we can add or subtract the equations to eliminate one of the variables and then solve for the remaining variable. In this case, we can multiply the first equation by 2 to get 4x in both equations:
4x + 6y = 16
4x - y = 11
Subtracting the second equation from the first, we get:
7y = 5
y = 5/7
Substitute y back into one of the original equations to solve for x:
2x + 3(5/7) = 8
2x + 15/7 = 8
2x = 8 - 15/7
2x = 56/7 - 15/7
2x = 41/7
x = 41/14
Therefore, by using the elimination method, we were able to solve for the values of x and y in the system of equations.