Objective - To solve a system of linear
equations by graphing.
System of Equations- Two or more equations
involving the same variables.
y  2x  1

x  y  5
y  2x 1
2
m2 
1
b  1
y
x y 5
x
(2,3) x
y  x  5
x
1
m  1 
1
b5
(2,3) is the solution to the system.
Solve.
x  y  1
2y  x  4

x  y  1
x
x
y  x 1
1
m  1 
1
b  1
(-2,1)
y
2y  x  4
x  x
2y  x  4
1
y x 2
x
2
1
m
2
b2
(2,1) is the solution to the system.
Solve.
2x  3y  3
x  6y  24

2x  3y  3
 2x
 2x
3y  2x  3
2
y  x 1
3
2
m
3
(-6, -3)
b 1
Check!
y
x  6y  24
x
x
6y  x  24
1
y
x4
x
6
1
m
6
b  4
(6,3) is the solution.
Solve the sytem below by graphing.
2x  3y  6
x  4y  8
y
x  4y  8
2x  3y  6
x
x
 2x
 2x
4y  x  8
3y  2x  6
1
2
y x2
y
x2
x
4
3
1
2
1
m
(4 , -1)
m
2
4
3
b2
b  2

1
Check! (4 ,1) is close to the solution.
2
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
120
100
total money
y  120  5x
x y
0 120
2 110
4 100
6 90
8 80
10 70
80
60
40
In 8
weeks
20
0
0
2
4
6
weeks
8
10
y  20  7.5x
x y
0 20
2 35
4 50
6 65
8 80
10 95