Solving Systems of Equations with Elimination

Elimination A

100

2x + 3y = -12 

-4x - 3y = 30

(-9,2)

200

3x + 4y = 16 

-5x - 4y = -16

(0,4)

300

-x + y = -1 

x + y = -3

(-1,-2)

400

-x - y = -10

 2x + y = 18

(8,2)

500

-5x + 5y = 20 

-5y + 2x = -38

(6,10)

Elimination B

100

-3x + 5y = -18 

4x + 5y = -11

(1,-3)

200

-3x + 5y = -8 

x + 5y = -24

(-4,-4)

300

5x + 4y = 20 

5x + y = 20

(4,0)

400

3x + 5y = 9 

3x + y = -15

(-7,6)

500

-2x + y = -8 

3y + -2x = -24

(0,-8)

Elimination C

100

-2x + 3y = 9 

4x - 4y = -4

(6,7)

200

2x + y = 21 

4x - 3y = 7

(7,7)

300

x + 2y = 2 

2x - 3y = 4

(2,0)

400

x + 4y = 10 

3x - 4y = 30

(10,0)

500

5y - x = 35 

3x + 5y = 75

(10,9)

Real World

100

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?

(35, 52) is the solution.

x is the number of hot dogs and x = 35. That means 35 hot dogs were sold.

y is the number of sodas and y = 52. That means 52 sodas were sold.

200

You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your bill totals $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?

(1.25, 2.5) is the solution

x = the price of 1 soft taco and x = 1.25.That means 1 soft taco costs $1.25.

y = the price of 1 burrito and y = 2.5. That means 1 burrito costs $2.50.

300

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

Senior citizen ticket: $8

Child ticket: $14

400

The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

Van: 18

Bus: 59

500

3x − 2y = 2 

5x − 5y = 10

(−2, −4)