Beyonce is solving a system of equations:
2x-3y=-2 and 4x+y=24
She multiplies the second equation by 3 and then adds the first equation to find 14x=-70, showing her that x=5. Beyonce finds that y=4. Thinking about this process, Beyonce says out loud,
“There are lots of ways I could go about solving this problem. I could do the method above or I could multiply the first equation by -2 and add the second. I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method?
1. What is the answer to Beyonce's question? Be sure to show work or explain reasoning.

2. Is the answer to (a) different if we have a system of two equations with no solutions? What if there are infinite solutions?

Cassie is traveling 675 miles today to visit her brother and his family. so far, she has stopped for gas three times. at the first stop, she put in 7.1 gallons of gas and paid $23.79. at her second stop, she put in 5.8 gallons of gas and paid $19.08. and, at the third stop, 6.6 gallons and paid $20.39. at which stop did casey pay the most for gas?

The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. complete parts (a) and (b) below. business degrees nonbusiness degrees total male 189131 634650 823781 female 169539 885329 1054868 total 358670 1519979 1878649 (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is nothing. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is nothing. (round to three decimal places as needed.)

Billy plotted −3 4 and −1 4 on a number line to determine that −3 4 is smaller than −1 4 is he correct? explain why or why not?