A student took a system of equations, multiplied the first equation by 2 and the second equation by 3, then added the results together. Based on this, she concluded that there were no solutions. Which system of equations could she have started with?

Answer 1

One possible system of equations that the student could have started with is:

2x + y = 6

3x + 3y = 9

If the student multiplied the first equation by 2 and the second equation by 3, she would get:

4x + 2y = 12

9x + 9y = 27

Adding the two equations together, she would get:

13x + 11y = 39

This equation does not have a unique solution, so the student would conclude that there are no solutions to the system.