Ch 5.1

Graphing Systems

Objective:

To solve a system of linear equations by graphing.

Definition

1) Graph both equations using any method (Table, Intercept, Slope-Intercept)

2) The (x, y) coordinate where the lines intersect is the solution.

Rules

System (of equations):Two or more equations involving the same variables.

Check Your Answers!Plug in the x and y solutions into BOTH equations to

verify that they both make TRUE statements.

€

y = 2x −1

€

y = −x + 5

€

x

€

y

€

(2,3)

€

(2,3) is the solution to the system.

y = 2x - 1y = -x + 5

Example 1

21

riserun

riserun

-1 1

€

y

€

(−2,1) is the solution to the system.

€

y = −x −1

€

y =12

x + 2

€

(-2,1)

y = -x - 1y = x + 21

2

€

x

Example 2

-1 1

riserun

riserun

12

€

x

€

y

€

(−6,−3) is the solution.

€

y =−16

x − 4

€

y =23

x +1

€

(-6,-3)

y = x + 123

y = x - 4-1 6

Example 3

23

riserun

riserun

-1 6

€

y

€

(412

,−1) is close to the solution.

€

y =14

x − 2

€

y =−23

x + 2

€

(412

,-1)

Check!

€

x

y = x + 2

y = x - 2

-2 3

14

Example 4

-2 3

riserun

riserun

14

Pam has $120 and is spending $5 every week.Lorenzo has $20 and is saving $7.50 every week.When will they have the same amount of money? Let x = # of weeks Let y = total money

Pam Lorenzo

€

y = 120 − 5x

€

y = 20 + 7.5x

weeks

tota

l mon

ey

0 2 4 6 8 10

120

100

80

60

40

20

0

In 8 weeks

-5 1

-10 2

= 7.5 1

15 2

=

30 4

=

Classworky = - x + 4

y = x - 4

1) y = - x - 3

y = -2x + 2

2)

€

x

€

y€

7

2

€

1

2

€

1

3

€

x

€

y

y = 5x - 2y = -x + 4

3) x + y = 37x + y = -3

4)

€

x

€

y

€

x

€

y

x + y = -36x + y = 2

5) 3x + y = 4x - 2y = 6

6)

€

x

€

y

€

x

€

y