At a restaurant, you eat 2 taco salads and drink two glasses of ice tea. Your friend eats 1 taco salad and drinks 1 glass of ice tea. The restaurant charges you $11 and your friend $6.50. Can you determine the prices of taco salads and ice tea? Explain.

Set up a system of equations that represent x as taco salads and y as iced tea:

2x + 2y = 11 (you)

x + y = 6.50 (your friend)

Solve the system of equations by solving one of the equations for a variable:

x+y = 6.50 (I solved for y):

y = 6.50 - x.

Plug this equation into the y of the first equation:

2x + 2 (6.50 - x) = 11

Solve for x:

2x + 13 - 2x = 11

2x cancels out:

13 = 11

No solution, so it is not possible to determine the prices of the items.