Systems of Equations

Word Problems

100

The length of a garden is 5 times its width.  Find the length and width if the perimeter is 72 feet.

W-6

L-30

200

A movie theater charges $7 for an adult’s ticket and $4.50 for a child’s ticket.  On a recent night, the sale of children’s tickets was three times the sale of adult tickets.  If the total amount collected for ticket sales was $2009, how many adults purchased tickets?

98 adults

300

The bill for a lunch of three hamburgers and two drinks is $9.67.  The bill for a lunch of four hamburgers and three drinks is $13.21.  What is the total cost of one hamburger and one drink?

$3.54

400

Bri made 13 logos in one day at work. Some were for sports and the rest were for beauty companies. The number of beauty logos she made was one more than twice the number of sport logos she made. How many sport logos (x) and beauty logos (y) did Bri make?

x- 4

y-9

500

Mark’s age plus twice David’s age is 48.  Three times Mark’s age plus 5 times David’s age is 132.  How old are Mark and David?

Mark-24

David-12

Graphing

100

y = x + 6

y = -x – 4

(-5, 1)

200

y = 3x

y = -x + 4

(1, 3)

300

y = (-1/5 x) -5

y= (2/5 x) -2

(-5,-4)

400

y – x = -7

y = -3x + 1

(2, -5)

500

y = ½x + 4

y = -2x – 1

(-2, 3)

Substitution

100

y=-2x 

-16x+ 7y =30

(-1, 2)

200

x = 2y + 4 

x + 6y = -4

(2, -1)

300

y = -4x + 5

y = 2x - 7

(2, -3)

400

x = 3y - 1

x + 2y = 9

(5 , 2)

500

y = 2x - 5

4x - y = 7

(1 , -3)

Elimination

100

−8x − 10y = 24 

12x + 10y = 4    

(7, -8)

200

x+7y=0

2x−8y=22    

(7, -1)

300

−3x + 3y = 3 

−5x + y = 13

(-3, -2)

400

2x + y = 20 

-6x - 3y = -60

Infinitely Many

500

3x + 4y = 10

2x − 4y = −2

(8/5 , 13/10)