Systems of Equationsby

GraphingUsing the calculator

A System of Equations: Consists of two linear equations We want to find out information

about the two lines: The exact location (x, y) where they

cross If the two equations are the same

line (infinite solutions) If they are parallel, then they don’t

cross (no solution)

One solution at a point (x, y)

Consistent & independent

Same line ---infinite solutions

Consistent & dependent

Parallel lines never cross----no solution

inconsistent

3 different possibleoutcomes

Solve

2 3

4 1

by ph1 Gra : Ex

y x

y x

They do cross….but Where?????

Steps:

1. Type both eqs into y=

2. Graph them

3.

4.

5. Answer:

2

Solve by Graph:

6

2

y

Ex

x

y x

They do cross….but Where?????

Steps:

1. Type both eqs into y=

2. Graph them

3.

4.

5. Answer:

Solve by

2

Grap

7

h

4

:

3

y x

x

Ex

y

They do cross….but Where?????

Steps:

1. Type both eqs into y=

2. Graph them

3.

4.

5. Answer:

3 2

3

Solve by Graph4 :

1

y

x

x

E

y x

They do cross….but Where?????

Steps:

1. Type both eqs into y=

2. Graph them

3.

4.

5. Answer:

8 4 4

Solve by

2

Gra

ph

:

1

5

x

x

E

y

x

y

8 4 4x y 2 1x y 2x 2x

2 1y x 8x 8x

2 1y x 4 4 4

4 8 4 y x