8th Grade Module 7: Systems Linear Equations

Vocab

100

Two lines that never intersect because lines are parallel; different y intercepts; (Example: 12=20)

solution of a system of equations, substitute, elimination, infinitely many solutions, no solution, complementary angles, supplementary angles

no solution

200

Same slope and y intercept; everything in both equations cancel each other out; (Example: 3=3 or 0=0)

solution of a system of equations, substitute, elimination, infinitely many solutions, no solution, complementary angles, supplementary angles

many solutions

300

A set of values that make all equations in a system true

solution of a system of equations, substitute, elimination, infinitely many solutions, no solution, complementary angles, supplementary angles

solution of a system of equations

400

Algebraic process of getting rid of a variable in a system of equations then adding equations together to solve

solution of a system of equations, substitute, elimination, infinitely many solutions, no solution, complementary angles, supplementary angles

elimination

500

Two angles added together to equal 180 degrees

solution of a system of equations, substitute, elimination, infinitely many solutions, no solution, complementary angles, supplementary angles

Supplementary Angles

Find Solution

100

6x+2y=114

-4x-2y=-84

(__,__)

(15, 12)

Y's cancelled.

2x=30

x=15

6(15)+2y=114

90+2y=114

2y=24

y=12

200

3x+2y=24

7x-2y=36

(__,__)

(6, 3)

Y's cancelled.

10x=60

x=6

3(6)+2y=24

18+2y=24

2y=6

y=3

300

x+y=6

x-y=12

(__,__)

(9, -3)

Y's cancel. 

2x=18

x=9

(9)+y=6

y=-3

400

x+y=7

2x+4y=18

(__,__)

(5, 2)

-2x-2y=-14

2x+4y=18

X's cancelled.

2y=4

y=2

x+(2)=7

x=5

500

3x-y=2

3x-2y=10

(__,__)

(-2, -8)

-3x+y=-2

3x-2y=10

X's cancel.

-y=8

y=-8

3x-(-8)=2

3x+8=2

3x=-6

x=-2

Many, No, One Solution

100

x+5=15

x+5=15

(no, many, or one solution)

many

SAME EQUATION

200

-2x-5y=25

2x+5y=100

(no, many, or one solution)

No solution

X's and Y's cancel but 25 and 100 do not cancel

0 = 125 (not true)

300

3x+5y=10

2x+5y=12

(no, many, or one solution)

one solution

3x+5y=10

-2x-5y=-12

Y's cancel, but not X's so you will have an x=number and y=number

400

x-3y=4

2x-6y=8

(no, many, or one solution)

many solutions

-2x+6y=-8

2x-6y=8

Everything cancels 0=0

500

4x-2y=-8

4x-2y=8

(no, many, or one solution)

no solution

-4x+2y=8

4x-2y=8

X's and Y's cancel but the 8's DO NOT 

0=16

Equations

100

What is the value of x?

2x=10

x=5

Divide both sides by 2

200

20x=400

x=20

Divide both sides by 20

300

Find value of x

5x+40=90

x=10

5x=50

Divide both sides by 5

400

4x + 5x + 3 =84

x=9

9x+3=84

9x=81

Divide both sides by 9

500

x/2 + 3=9

x=12

x/2=6

Multiply both sides by reciprocal (multiply by 2)

Misc. Valentine's Day

100

What is the most popular flower to give on Valentine's Day?

rose

200

Name of the winged child that shoots people with an arrow to fall in love

Cupid

300

Two most popular valentines candy?

chocolate, fun dip, nerds, candy hearts, candy corn, skittles

Chocolate and Candy Hearts

400

Fill in the blank

Be ______

Mine

500

Who receives the most Valentine's Day cards?

teachers