The total cost for a bucket of popcom and 4 movie tickets is $56. The total cost for the same size bucket of popcorn and 6
movie tickets is $80. The cost of a bucket of popcorn is $8. Which equation represents the relationship between y, the total
cost of the popcom and movie tickets, and x, the number of movie tickets that are purchased?

Consider the system: y = 3x + 5 y = ax + b what values for a and b make the system inconsistent? what values for a and b make the system consistent and dependent? explain

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Complete the equation of the line through (−10,3) and (−8,−8). use exact numbers.