Linear Systems

Graphing Systems

100

If two lines cross at (-2, 2), what is the solution to the lines?

one solution, (-2,2)

200

Graph the following equations and determine the number of solutions. 

y = 15x + 30

y = 20x + 15 

One solution. 

300

If you graph two lines, and they are right on top of each other (you only see one line), how many solutions do they have?

Many

400

Graph: 

y = 2x + 3

y = 2x - 4

No solution, same slope/does not touch 

500

What is Mrs. Shane's favorite color?

BLUE

Substitution

100

If you find x in the solution, you must find _____, AND that means the lines have ______ solution(s)

Find: y

One solution 

200

Solve the following linear systems: 

x = -y + 1

3x - y = 15

(4, -3)

300

Solve:

y = x + 5

3x + y = 25

(5,10), one solution 

400

x - y = 1

3x = 3y + 3

Many solutions

3(y + 1) = 3y + 3

3y + 3 = 3y + 3

500

2x - y = 8

y = 2x - 3

2x -2x - 3+ 8

-3 = 8

No solution 

Elimination

100

4x + 6y = 32

3x - 6y = 3

One solution, (5, 2)

200

4y + 3x = 22

-4y + 3x = 14 

One solution, (6,1)

300

6x - 3y = 27

2x - 3y = 11

one solution, (4, -1)

400

What does it mean for two lines to have a no solution?

The two lines will NOT touch on a graph 

500

What position did Mrs. Shane play in softball? 

2nd base (and pitcher)