Systems of Equations

Graphing

100

y = 2x - 3

y = -3x + 2

(1, -1)

200

y = -x + 1

x = 3

(3, -2)

300

y = 4x + 1

y = x - 2

(-1, -3)

400

-2x - y = 1 

-6x = 3y + 3

Infinite Number of Solutions

500

x - 2y + 8 = 0 

-6 - 2y = -x

No Solution

Substitution

100

y = 6x − 11

−2x − 3y = −7

(2, 1)

200

2x − 3y = −1

y = x − 1

(4, 3)

300

y = 5x − 7

−3x − 2y = −12

(2, 3)

400

−4x + y = 6

−5x − y = 21

(-3, -6)

500

−2x − y = −9

5x − 2y = 18

(4, 1)

Elimination

100

−4x − 2y = −12

4x + 8y = −24

(6, -6)

200

x − y = 11

2x + y = 19

(10, -1)

300

−2x − 9y = −25

−4x − 9y = −23

(-1, 3)

400

8x + y = −16

−3x + y = −5

(-1, -8)

500

3 + 2x − y = 0

−3 − 7y = 10x

(-1, 1)

Any Method

100

y = -1/4 x − 4

y = 5/4 x + 2

(-4, 3)

200

y = 2x + 3

y = −4x − 3

(-1, 1)

300

x + 8y = −15

7x + 8y = −9

(1, −2)

400

−9x − 3y = −2

y = −3x − 4

No Solution

500

−6x − 9y = 0

−24x = 36y

Infinite Number of Solutions

Final Jeopardy

100

Solve the system of inequalities by graphing:

x + y ≥ −3

x + y ≤ 3

Graph Shown on Board