Solving by Graphing
Solving by Substitution
Solving by Elimination
Mixed
Story Problems
100

y = 2

y = -2x - 4

(-3, 2)


100

y = 3x

2y - 5x = 4

(4, 12)

100

x - 2y = -10

-x - 2y = -14


(2, 6)

100

What method would be best to solve? Solve the system

x + y = 1

2x + 4y = 0


Substitution or elimination(Could argue for both)

(2, -1)

100

The sum of two numbers is 14. Their difference is 2. Find the numbers.

The numbers are 6 and 8

200

y = -x + 4

y = 5/3x - 4

(3, 1)

200

y = -4x - 1

y = -2x + 1



(-1, 3)

200

-5x - 4y = 11

-2x + 4y = 10

(-3, 1)

200

What method would be best to solve? Solve the system

y = 3x - 1

y = -2x + 4

Substitution or graphing(Could argue for both)

(1, 2)

200

Mrs. Frazier ordered lunch for herself and several (of her fabulous math) coworkers on Monday and Tuesday.  On Monday, she paid $7 for five sandwiches and four sodas.  On Tuesday, she paid $6 for four of each.  Find the price of each item

$1 per sandwich

$0.50 per soda

300

y = 3/2x - 3

y = -1/6x + 7

(6, 6)

300

6x - 2y = -16

x - 2y = 9

(-5, -7)

300

-14x + 8y = 14

-7x + 6y = 21

(3, 7)

300

What method would be best to solve? Solve the system

-11x - 5y = -11

-x - 3y = -1

Elimination

(1, 0)

300

Emily's school is selling tickets to a choral performance. On the first day of ticket sales the school sold 8 adult tickets and 3 child tickets for a total of $136. The school took in $124 on the second day by selling 2 adult tickets and 12 child tickets. Find the price of an adult ticket and the price of a child ticket.


Each adult ticket costs $14 and each child ticket costs $8

400
3 - 2x = y

2y = x - 14

(4, -5)

400

-8x + 2y= - 20

3x + 6y = -6

(2, -2)

400

-2x - 12y = 22

-3x + 9y = 6

(-5, -1)
400

What method would be best to solve? Solve the system

6x - 20y = -14

-x - 10y = 29

Substitution or Elimination(Could argue for both)

(-9, -2)

400

Ryan and Jimmy each improved their yards by planting rose bushes and ivy. They bought their supplies from the same store. Ryan spent $176 on 10 rose bushes and 14 pots of ivy. Jimmy spent $92 on 6 rose bushes and 5 pots of ivy. What is the cost of one rose bush and the cost of one pot of ivy?

Each rose bush costs $12 and each pot of ivy costs $4

500

-x = 4y + 4

4y + x = -4

No Solution (Parallel lines)

500

-10x + 12y = 0

5x - 6y = -3

No Solution

500

12 + 3x = 8y

2x = 9y - 8

(-4, 0)

500

What method would be best to solve? Solve the system

12x + 9y = -27

4x + 3y = -9

Elimination

Infinite number of solutions(if graphed, we would have the same line)

500

Brenda and Mofor are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Brenda sold 9 boxes of oranges and 13 large boxes of oranges for a total of $306. Mofor sold 5 small boxes of oranges and 4 large boxes of oranges for a total of $112. Find the cost of one small box of oranges and one large box of oranges.

The cost for a small box of oranges is $8 and the cost for a large box of oranges is $18

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