Systems Review

Vocabulary

100

What we call letters in math 

What is a variable? 

200

A number without a variable attached 

What is a constant? 

300

This linear equation gives you the slope and the y-intercept. 

What is slope intercept form? 

400

Terms that have the same variable raised to the same power. 

What are like-terms? 

500

This is where we find the solution to a system on a graph.

What is an intersection point? 

What comes next?

100

-3+4*7÷(8-4)

-3+4*7÷(4)

...

4*7

200

8x+2x=10 

Add like terms

10x=10

300

4y+3(y+2)=6x

distributive property: distribute the 3  

400

10x=7x+3(y-6)

10x=7x+3y-18

.... 

subtract 7x from both sides 

500

2x+4y=12

2x-3y=5

7y=7

y=1 

Plug 1 in for y in one of our equations. 

What strategy do we use?

100

y=3x-2

x+2y=4 

Substitution

200

y+13x=12

y-5x=-6 

Elimination-

eliminate the y terms first 

300

x=2y+13 

3y+6x=30 

Substitution- 

substitute (2y+13) in for x in the second equation 

400

5x+2y=26

-5x+y=-15 

Elimination 

500

4x+7y=13

2x+10y=30 

Elimination- 

If we double the second equation, then we can eliminate the x terms 

How do we graph it?

100

y=(1/3)x+3 

y-int= 3

Rise: 1

Run: 3 

200

y=-1/4x-3 

y-int.=-3

rise=-1

run=4

300

y=3/5x 

y-int=0

rise=3

run=5 

400

3x+5y=15 

x-int.= 5

y-int.=3 

500

-6x+y=15+3

x-int.=-3

y-int.=18

Is it a solution?

100

5x+3=18

x=-3 

No:

5(-3)+3=18

-15+3=18

-12=18

200

7x+5y=29

(2,3) 

Yes: 

7(2)+5(3)=29

14+15=29

29=29

300

y=4x+2

3y=15

(1, 5) 

No:

5=4(1)+2

5=4+2

5=6

400

3x+9y=12

x+y=4 

(4,0) 

Yes:

3(4)+9(0)=12                 4+0=4

12+0=12                          4=4

12=12

500

y=5-4(3x-7) 

y=x+7 

(2,9) 

Yes:

9=5-4[3(2)-7]                 9=2+7

9=5-4(6-7)                        9=9

9=5-4(-1)

9=5+4

9=9