Question

For the following equations, enter U if the equation has a unique solution, N if it has no solution, and I if it has infinitely many solutions.

1/8x+5 = 1/5x+5 ??

1/8x+5 = 2/8x+5 ??

Answer 1

Do they have the same slope?

Answer 2

yes

Answer 3

The two questions to ask are: do the two sides have the same slope, and are they the same line. If they are the same line, there are infinitely many solutions. That means the two equations are equal. If they have the same slope and aren't the same line, then they are parallel, and therefore they never meet, therefore they have no solutions (they are not equal anywhere). If neither is true, then the two lines intersect at some single point.

Answer 4

you have 2 different equations, so you'll be asking these questions about each one. None of them have the same slope. Therefore they each have only 1 solution.