1. Find all solutions of the given system of equations and check your answer graphically.

2x - 3y = 1

6x - 9y = 3

1. Use Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand, and others using technology.

-1/2x + y-1/2z = 0

-1/2x - 1/2y + z = 0

x - 1/2y - 1/2z = 0

1. Gauss-Jordan row reduction to solve the given systems of equation. We suggest doing some by hand, and others using technology.

x - 3y - 2z - w + 1

x + 3y + z+2w = 2

2x - z + w = 3

1. The Enormous State University History Department offers three courses, Ancient, Medieval, and Modern History, and the chairperson is trying to decide how many sections of each to offer this semester. The departmentis allowed tooffer 45 sections total, there are 5,000 students who would like to take a course, and there are 60 professors to teach them. Sections of Ancient History have 100 students each, sections of Medieval History hold 50 students each, and sections of Modern History have 200 students each. Modern History sections are taught by a team of 2 professors, while Ancient and Medieval History need only 1 professor per section. How many sections of each course should the chair schedule in order to offer all the sections that theyare allowed to, accommodateall ofthe students, and give one teaching assignment to each professor?