Solving Systems Of linear Equations

Graphing

100

y = 2x +2 

y = x - 1

What is (-3,-4)

200

-2x+3y=-9 

x+y=2

What is (3.-1)

300

y= -3x - 3 

y= -3

What is (0,-3)

400

y= 4x -10 

y = 1/3x + 1

What is (3,2)

500

y= 1/2x +5 

y= -5/2x - 1

What is (-2,4)

Elimination by Adding

100

12x - 3y = 30 

2x + 3y = 12 

What is (3,2)

200

3x - 5y = -9 

4x + 5y = 23

What is (2,3)

300

2x - 3y  = -13 

5x - 12y = -46

What is (-2 , 3)

400

-2x + 3y = 6 

3x - 5y = -11

What is (3,4)

500

3x + y = 10 

2x – y = 5

What is (3,1)

Elimination by Subtraction

100

3x - y =4 

2x - y =1

What is (3,5)

200

3x + 4y =20 

3x + 2y =16

What is (4,2)

300

16x + 12y = -4 

15x + 12y = 3

What is (-7, 9)

400

x - 2y = 14 

x + 3y = 9

What is (12,-1)

500

x + 4y = 12 

x + 3y = 7

What is (-8,5)

Substitution

100

y= -2 

4x - 3y = 18

What is (3,-2)

200

y = 5x − 7 

−3x − 2y = −12

What is (2, 3)

300

y = −3 +5x

3x − 8y = 24

What is (0, −3)

400

y−5x = −2

−3x + 6y = −12

What is (0, −2)

500

−3x + 3y = 3 

y−5x = 13

What is (−3, −2)

Word Problems

100

Kristin spent $131 on shirts.  Fancy shirts cost $28 and plain shirts cost $15.  If she bought a total of 7 shirts, find how many of each shirt that she bought.  Use the equations below, where x represents number of fancy shirts and y represents number of plain shirts.

x + y = 7

28x + 15y = 131

2 fancy shirts and 5 plain shirts

200

A class of 195 students went on a field trip.  They took 7 vehicles, some cars and some buses.  Find the number of cars and the number of buses they took if each car can hold 5 students and each bus can hold 45 students.  Let x represent number of cars and y represent number of buses.

(HINT:  your first equation should be represent the total number of vehicles that were taken; the second equation should represent the total number of students)

3 cars and 4 buses

300

There are 13 animals in a barn.  Some are chickens and some are pigs.  There are 40 legs in all.  How many of each animal are there?  Let x represent chickens and y represent pigs.  Use the equations below.

x + y = 13

2x + 4y = 40

6 chickens and 7 pigs

400

A farmhouse shelters 10 animals.  Some are pigs and some are ducks.  Altogether there are 36 legs.  How many of each animal are there?  Let x represent pigs and y represent ducks.

2 ducks and 8 pigs

500

A farmhouse shelters 11 animals.  Some are goats and some are ducks.  Altogether there are 34 legs.  How many of each animal are there?  Let x represent ducks and y represent goats

5 ducks and 6 goats

Number of Solutions

100

9x + 3y = 15

27x + 9y = 9

No solution

200

-8x + 2y = 8

4x + 8y = -4

One Solution (-1, 0)

300

-14x - 16y = 24

-7x - 8y = 12

Infinitely Many Solutions

400

Person A leaves at 3p and travels at 4mph. Person B leave at 4p and also travels at 4mph.

No Solution

500

Train A leaves the station at 2p and travels at a constant speed of 40mph.  Train B leaves the station at 4p and travels at a constant speed of 45 mph.  

One Solution