Explain how you can determine that the following system has one unique solution – without actually solving the system.2x+y=4 2y=6-2x

Answer:  The slopes are different

To compare the lines put them both in slope intercept form. The first equation will be y = -2x + 4 and the second equation will be y = -1x + 6. The slopes of the 2 graphs are different. These means that they are going in different directions. Therefore, they will cross a one unique point.