Systems of Equations

Elimination

100

Solve the following simultaneous equations by using the elimination method: 11x + 6y = 79 and 11x + 3y = 67

What is (5,4) OR What is x=5 and y=4

200

Solve the following simultaneous equations by using the elimination method: 2x + 3y = 15 and 4x - 3y = 3

What is (3,3) OR What is x=3 and y=3

300

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Greenville Nail Salon is having a special this month on services. Over the weekend, they performed 28 manicures and 39 pedicures, bringing in a total of $1,389 in receipts. So far this week, they have administered 16 manicures and 39 pedicures, with receipts totaling $1,245. How much does the salon charge for each service?

What is The salon charges $12 for manicures and $27 for pedicures.

400

An administrative assistant is making some copies. She made 46 one-sided copies and 35 two-sided copies for the V.P. of Marketing, which took a total of 221 seconds. Next, she made 48 one-sided copies and 35 two-sided copies for the Director of Sales, which took 223 seconds. How long does it take to make each type of copy?

What is It takes 1 second to make a one-sided copy and 5 seconds to make a two-sided copy.

500

In order to burn calories and lose weight, Meghan is trying to incorporate more exercise into her busy schedule. She has several short exercise DVDs she can complete at home. Last week, she burned a total of 706 calories by doing 5 body sculpting workouts and 4 yoga sessions. This week, she has completed 3 body sculpting workouts and 1 yoga session and burned a total of 299 calories. How many calories does each workout burn?

What is A body sculpting workout burns 70 calories and a yoga workout burns 89 calories.

Substitution

100

Solve by substitution. 2x + 3y = 4 y = 5x – 27

What is (5,-2) OR What is x=5 and y=-2

200

Solve the following system by substitution. c – 3d = 2 3c + d = 16

What is (5,1) OR What is x=5 and y=1

300

Meredith and Vicky both went bowling last weekend, but not together. Meredith went during open bowling time, paying $2 for shoe rental and $3 per hour. Vicky went on family night, when each hour was $1 and shoe rental was $16. As it turned out, they played for the same number of hours and spent the same amount. How much did each one spend? How many hours did each one bowl?

What is Meredith and Vicky each spent $23 and bowled for 7 hours.

400

Professor Preston is grading papers in the teachers' lounge. He has already finished grading 6 assignments, and is grading 3 more assignments per hour. His teaching assistant just came in to help him. She can grade at a rate of 4 assignments every hour. At some point, they will be finished and will have graded the same number of papers. How long will that take? How many assignments will they each have graded?

What is In 6 hours, both Professor Preston and his assistant will have graded 24 assignments.

500

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. A charity is considering the possibility of having a benefit night at two different restaurants. The owner of the local Italian restaurant has offered to make a donation of $969 and $2 per diner that night. On the other hand, the owner of the Mexican restaurant has said he could contribute $433 plus $4 per diner. Based on the number of diners who have promised to participate in the event, it appears that each restaurant would donate the same total amount. How many diners promised to participate? How much would each restaurant donate?

What is With 268 diners promising to participate, each restaurant would donate $1505.

Graphing

100

Graph the following system and find its solution. Also verify algebraically. x + 4y = –1 x + 3y = 0

What is (3,-1).

200

Graph the following system of equations and find the solution. y=(1/2)x-3 3x+2y=2

What is (2,-2).

300

Graph the system of equations and find the solution. y=-3x+2 y=2x+3

What is (1,-1).

400

Michaela’s mom is trying to decide between two plumber companies to fix her sink. The first company charges $50 for a service call, plus an additional $36 per hour for labor. The second company charges $35 for a service call, plus an additional $39 per hour of labor. At how many hours will the two companies charge the same amount of money?

What is The companies will charge the same amount at 5 hours.

500

The members of a cooking club are making cakes, which they will sell at a street fair for $15 apiece. It cost $30 for a booth at the fair, and the ingredients for each cake cost $5. At some point, the club members will sell enough cakes so that their sales cover their expenditures. How much will the sales and expenditures be?

What is 45 dollars

Strictly Problems

100

Solve graphically: 4x - 6y = 12 2x + 2y = 6

What is (3,0)

200

Solve this system of equations 3y - 2x = 11 y + 2x = 9

What is (2,5) OR What is x=2 and y=5

300

Solve the following system using addition. 2x – y = 9 3x + 4y = –14

What is (2, -5) OR What is x=2 and y=-5

400

Solve this system of equations 4x + 3y = -1 5x + 4y = 1

What is (-7,9) OR What is x=-7 and y=9

500

Solve the following system using addition. 4x – 3y = 25 –3x + 8y = 10

What is (10,5) OR What is x=10 and y=5

Strictly Word Problems

100

A group of adults and kids went to see a movie. Tickets cost $6.50 each for adults and $4.50 each for kids, and the group paid $44.50 in total. There were 5 fewer adults than kids in the group. Find the number of adults and kids in the group.

What is 2 adults and 7 kids were in the group.

200

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

What is 35 hot dogs were sold and 52 sodas were sold at the basketball game.

300

All of the 3rd grade teachers and students from Oak went on a field trip to an art museum. Tickets were $5.00 each for teachers and $3.50 each for students, and the group paid $46.50 in total. A few weeks later, the same group visited a science museum where the tickets cost $10.00 each for teachers and $10.50 each for students, and the group paid $124.50 in total. Find the number of teachers and students on the field trips.

What is 3 teachers and 9 students were on the field trip.

400

Calvin has $8.80 in pennies and nickels. If there are twice as many nickels as pennies, how many pennies does Calvin have? How many nickels? In this kind of problem, it's good to do everything in cents to avoid having to work with decimals. So Calvin has 880 cents total. How many of each coin did Calvin have?

What is Calvin had 80 pennies and 160 nickels.

500

$6000 is divided between two accounts, one paying $4%$ interest and the other paying $3%$ interest. At the end of one interest period, the interest earned by the $4%$ account exceeds the interest earned by the $3%$ account by $65. How much was invested in each account?

What is $2500 was invested at 3% and $3500 was invested at 4%.