Unit 5 8th Grade Math

Elimination

100

3x+3y =6 

-3x-y=-6

3x+3y =6 

-3x-y=-6

0=4y=12

4y=12

y=3

3x-y=-6 

3x-3=-6

3x=-3

x=-1

200

-7x+ y=-19                  

-2x +3y = -19

21x-3y=57

2x+3y=-19

19x/19 =38/19

x=2

-7(2) +y =-19                multiply by -3

-14+y=-19

+14      +14

y/y =-5/1

y=-5

300

4x-2y=-12 

4x+8y =-24

4x-2y=-12 

4x+8y =-24

      6y= 36

36/6 =6   y=6

4x - (2x6) =-12

 4x/4 = 24/4

x=6

400

 -2x-9y= -25

 -4x -9y= -23                                             

-2x-9y=-25

4x+9y =23

2x=-2 

2x/2 =-2/2 = -1

  -2(-1) - 9y =-25    multiply the bottom by -1

2-9y = -25

-2        -2

9y/9 = 27/9 

y= 3

500

-6x+ 6y =6 

-6x +3y = -12 

multiply by top by -1

6x-6y=6

-6x-3y=-12\

-3y/-3 = 6/-3

y= -2

6x+6(-2)=6

6x-12=6

6x/6= 18/6

x=3

Exponents

100

8^-1

1/8

200

11^-2

121

300

25³

15625

400

7⁸ x 7⁵

7¹³

500

10¹⁷ x 10³

10²⁰

Pythagorean Theorem

100

24²+7²=C²

24² +7² = C²

576 + 49

625=c²

25=c²

200

30²+ 40²=C²

30²+ 40² =C²

900+ 1600=

2500= C²

50=C²

300

9²+40²=41²

9²+40²=41²

81+1600=1681

1681=1681

400

12²+15²=C²

12²+15²=

144+225=369

C²=19.2

500

a²+80²= 200²

a²+80²= 200²

a²+6400= 40000

40000-6400= 33600

 a²= 183.30

Volume

100

V= 3.14 x 2² x 3

 3.14 x 2² x 3

3.14 x 4 x 3

V=37.69in³

200

V= 3.14 x 6² x 11

3.14 x 6² x 11

3.14 x 36 x 11

V= 1244.07in³

300

V= 3.14 x 5² x 16

 3.14 x 5² x 16

3.14 x 25 x 16

1256cm³

400

V = 1/3 x 3.14 x 3² x 6

1/3 x 3.14 x 3² x 6 

1/3 x 3.14 x 9 x 6

V= 56.54cm²

500

V= 1/3 x 3.14 x 18² x 20

1/3 x 3.14 x 18² x 20

1/3 x 3.14 x 324 x 20

V= 6785.84in³

Inputs and Outputs

100

y=3x+2

X: -2 -1 0 1 2

Y; -4  -1 2 5 8

200

y= 3 -2x 

X= 1  2  3  4  5  8 

Y= 1 -1 -3  -5 -7  -13

300

What are Inputs?

Inputs are the variables or things that are put in, used or operated inside a function to obtain an output.

400

What are outputs?

The output is what comes out of the function.

500

y=2x-7

x=  0  1   2   3  

y= -7 -5 -3 -1