Systems of Equations

Starts with "S"

100

More than one equation to be solved at the same time is know as this.

System of Equations

200

The ratio of rise to run.

Slope

300

The answer to an equation or system of equations.

Solution Set

400

y = mx + b is more formally known as this:

________-__________ form.

Slope-Intercept Form

Graphing

100

Solve by graphing:

     y = x + 4

     y = 2x + 5

(-1, 3)

200

Solve by graphing:

      y = 3x - 2

      y = -x - 2

(0, -2)

300

Solve by graphing:

   y = (1/3)x - 3

   2x - y = 8

(3, -2)

400

Solve by graphing:

 

   y - 3x = 3

   y = 3x - 2

No solution

Substitution

100

Solve by substitution:

   x = 4y

  2x + 3y = 22

(8, 2)

200

Solve using substitution:

     y = x - 2 

    3x - y = 16

(7, 5)

300

Solve using substitution:

    y = 3x - 1

    7x + 2y = 37

(3, 8)

400

Solve using substitution:

   3w - 2p = 4

   p = 2w - 1

p = -5

w = -2

Elimination

100

Solve using elimination:

   r + s = -6

   r - s = -10

r = -8

s = 2

200

Solve using elimination:

   8a + 5b = 9

   2a - 5b = -4

a = 0.5

b = 1

300

Solve using elimination:

   2x - 4y = 12

   2x + 2y = 6

(4, -1)

400

Solve using elimination:

    3x + 2y = 10

   -2x + 4y = 4

(2, 2)

Word Problems

100

Write a system of equations to model the word problem below:

Two zookeepers are in charge of feeding the animals. The first zookeeper is responsible for feeding the land animals, and the second zookeeper is responsible for feeding the animals in the water exhibit. The first zookeeper has already fed 4 animals and is feeding 1 additional animal per hour. The second zookeeper has already fed 1 animal and is feeding 2 additional animals per hour. After how many hours will the two zookeepers have fed the same number of animals?

y = total animals fed

x = number of hours

y = 1x + 4

y = 2x + 1

200

Write a system of equations that could be used to solve the word problem:

JoAnn is measuring her plants. The first plant started out at two inches tall and grows at a rate of five inches per day. But, oh no!  Her second plant is starting to wilt. It began at ten inches, but is shrinking at a rate of three inches per day. How long will it take for her plants to be the same height? 

y = total plant height

x = number of days

y = 5x + 2

y = -3x + 10

300

Write a system of equations that could be used to solve the problem below:

The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

a = adult

c = child

a + c = 2200

$4a + $1.5c = $5050

400

Write a system of equations to model the following:

Harold had a summer lemonade stand where he sold small cups of lemonade for $1.25 and large cups for $2.50. If Harold sold a total of 155 cups of lemonade and collected a total of $265, how many cups of each type did he sell?

S = small lemonade

L = large lemonade

$1.25S + $2.50L = $265

S + L = 155