Graph and solve the following system of equations.

Problem 1

x - y = 2

-2x + y = 1

Solve the following independent system of equations.

Problem 2

5 x - 5 y = -15

7 x - 5 y = -5

Problem 3

3 x - 2 y = 3

8 x - 9 y = -14

Problem 4 - 7

Noah is writing an exam for his 8th-grade students. The exam is worth 100 points and Noah wants 35 questions on the exam. He plans to mix short answer questions, worth 3 points, with multiple-choice questions worth 2 points.

Create a system of equations to tell us how many of each type of question Noah can have on the test.

Let x= the number of short answer questions and y= the number of multiple-choice questions

4.Create an equation for the number of questions on the test.

5.Create an equation for the number of points on the test.

6.How many short answer questions should Noah put on the exam?

7.How many multiple-choice questions should Noah put on the exam?

Problem 8 - 11

The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people.

Create a system of equations to find the smallest number of busses the orchestra can rent.

Let x= the number of busses and y= the number of vans

8. Create an equation representing the number of vehicles needed.

9. Create an equation representing the total number of seats in vehicles for the orchestra members.

10. How many busses does the orchestra need to rent?

11. How many 12-passenger vans does the orchestra need to rent?