Algebra 1 Module 9

Solving Systems by Graphing

100

When a graph consists of two parallel lines, the system of equations has __________ solution.

No

200

When two lines that are graphed have the same equations, there are _______________ solutions. 

infinitely many

300

y=x+4

y=-x+6

(1, 5)

400

y=x+4

-x+y=4

infinitely many solutions 

500

y=2x+8

-2x+y=3

No solution

Solving Systems by Substitution

100

y=3

y=11-2x

(4,3)

200

y=x+3

y=-x+7

(2,5)

300

x+y=4

-x-y=6

No solution

400

4y=1

8x-4y=3

(1/2, 1/4)

500

x-3y=6

4x-12y=24

Infinitely many solutions

Solving Systems by Elimination

100

To be able to eliminate a variable, the like terms have to have the ___________ number and __________ sign. 

Same, Opposite

200

-2x+y=3

3x-y=-2

(1, 5)

300

3x+2y=10

3x-y=-2

(6, -4)

400

x+4y=20

-3x+7y=35

(0, 5)

500

2x+3y=12

6x+4y=26

(3, 2)

Final

300

Solve this system three ways

1. Graphing

2. Using Substitution 

3. Using Elimination

-2x+3y=4

3x+3y=9

(1, 2)