What is the solution to the system of equations? 3x − 6y = −12
−x + 2y = 8

a.) Use the substitution or elimination method to solve the system of equations.

b.) Based on your answer what do you know about the two lines in this system of equations on a graph? Are the lines parallel, do they intersect at a point or are they the same line?

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."

High schoolmathematics 5 points keith is the leading goal scorer for a team in an ice hockey league. last season, he scored 42 goals in 82 games. assuming he scores goals at a constant rate, what is the slope of the line that represents this relationship if the number of games is along the x-axis and the number of goals is along the y-axis?

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.