Systems

Solve by Graphing

100

y= 2x-8

13x+2y=18

(2,-4)

200

3x+7y=-63

x-y=-1

(-7,-6)

300

3x-2y=10

x=2

(2,-2)

400

-6y=36-x

4x-3y=-3

(-6,-7)

500

-12x=30y+60

2x+5y=20

No Solution

Elimination

100

3x+y=11

5x-y=21

(4,-1)

200

2x-9y=-51

2x-3y=-9

(6,7)

300

5x+12y=-34

2x+4y=-12

(-2,-2)

400

12y = 17- 9x

-4y - 3x = 31 

No solution 

500

Solve the system of three variables: 

x - 7y +3z = 17

5x + 2y -2z = -57

3x - 10y - z= -11

(-9 , -2 ,4 )

Congrats if you got it right, an extra 400 points will be given.

Substitution

100

y=-4x-9

7x+4y=-27

(-1,-5)

200

3x - 7y = -18

4x - 2y = -24

(-6 , 0)

300

8x + y = -39

2x -5y = 27

(-4 , -7)

400

12y = 17 - 9x

-4y - 3x = 31

No solution 

500

11y + 1 = -6x

0 = 43 - 7x - 4y

(9, -5)

Applications

100

Courtney has a total of 88 stamps worth $15.56. Some are 25 cents stamps and some are 2 cents stamps. How many of each does she have?

Courtney has 60- 25 cent stamps and 

28- 2 cents stamps

200

Tom put 18 gallons of mid grade gas in his truck and filled his empty five gallon gas tank with regular gas for his lawnmower at home. He spent $59.91. The following week, he put 14 gallons of mid grade gas in his truck and topped off his five gallon tank with just one gallon of regular gas. If he paid $39.75 and the prices remained the same, find the price per gallon of mid grade regular gas.

Regular cost $2.37/gal and mid grade is $2.67/gal.

300

Katys favorite ride at the amusement park are the rollercoaster and waterslide. The wait time for the rollercoaster is 25 minutes and the wait time for the water slide is 10 minutes. If she went on 12 rides total and waited three hours in line, how many times did she go on each ride?

Hint: One of the equations is x+y=12

Rollercoaster - 4 

Waterslide - 8

400

Casey bought a 15.4 pound turkey and an 11.6 pound ham for Thanksgiving and paid $38.51. Her friend Jane bought a 10.2 pound turkey and a 7.3 pound ham from the same store and paid $28.84. Find the cost per pound of turkey and the cost per pound of ham. 

Turkey cost $1.19 per pound and ham cost $1.74 per pound

500

Owen has a collection of nickels and quarters worth $8.10. If the nickels were quarters and the quarters were nickels, the value would be $17.70. Find the number of each coin. 

67 nickels and 19 quarters 

Linear/System Inequalities

100

Solve the inequality: 2x-6y > 36

y < 1/3x - 6 

200

How would you graph: x< -4

Dotted or solid line?

To the left or to the right? 

Dotted line and shaded to the left 

300

Change the equation into slope intercept form:

x - 6y < -12

Dotted or solid line?

Shade above or below?

y > 1/6x + 2

Dotted line

Shade above 

400

Write a system of linear inequalities to represent the situation below and put it into slope intercept form:

To raise money for the football team, Eric is selling chocolate. Small chocolate bars sell for $4 each and king sized chocolate bards sell for $6 each. He needs to earn at least $300 to attend camp. He will also get brand new gear if he sells at least 60 bags total of any combination. 

For an extra 200 points state whether the graphs will be dotted or solid lines and whether to shade above or below.

4x + 6y >= 300 --> y= -2/3x + 50

x + y >= 60 ---> y >= -x + 60

Both graphs will be solid lines and shaded above

500

Luke needs at least $1.60 in stamps to mail a package. He has 20 cent stamps ($0.20) and 4 cent stamps ($0.04). He can use no more than twenty-five 4 cent ($0.04) stamps as he only has one book left. 

Write the two systems of linear inequalities to represent this situation and convert the equations into slope intercept form.

State whether you will use a dotted or solid line for each equation and which way to shade.

0.20 x + 0.04y >= 1.60

y <= 25

SLOPE

y >=  -5x + 40

y <= 25

Equation 1 and 2 will have solid lines. For equation 1 you will shade above, for equation 2 you will shade below.