Download 6.1 Solving systems by graphing

6.1 Solving systems by graphing
Solving systems by graphing and
analyzing special systems
Solution:
An ordered pair that makes the
equation true.
Example:
x+y=7
5+2=7
What are some possible
solutions?
The solutions are always written in ordered
pairs.:
(5,2)
3+4=7
(3,4)
-1 + 8 = 7
(-1,8)
-10 + 17 = 7
(-10,17)
How many
more
solutions are
there?
System of Equations
Definition: a set of two or more equations that
have variables in common.
Any ordered pair that makes ALL the
Solution:
equations in a system true.
Example of
a system:
y = 3x + 1
y = -2x - 4
Solution for this system: (-1,-2)
Verify (check your answer) whether or not the given
ordered pair is a solution for the following system of
equations. (same system as previous slide)
( -1,-2)
y = 3x + 1
y = -2x -4
( -2 ) = 3 ( -1 ) + 1
-2 = -3 + 1
( -2 ) = -2(-1 ) - 4
-2 = 2 - 4
Is (-1, -2) a solution? explain
YES, because the ordered pair makes both
equations true.
Find the solution for the following system.
y = 3x + 1
m= 3; b = 1
y = -2x - 4
5
m= -2; b = -4
Solution: (-1, -2)
0
-5
-5
0
5
Find the solution for the following system.
2x + y = 3
y = -2x + 3
m= -2; b = 3
y = 3x - 2
5
m= 3; b = -2
0
Solution: (1, 1)
-5
-5
0
5
Find the solution for the following system.
y=½x+1
m= ½; b = 1
2y – x = 2
5
x –int= -2
y –int= 1
0
Solution:
Infinitely many
solutions (because
the lines are the
same)
-5
-5
0
5
Find the solution for the following system.
y = 2x + 2
m= 2; b = 2
y = 2x - 1
m= 2; b = -1
5
Solution:
No solution
0
(because the lines
are parallel)
-5
-5
0
5
Systems with infinitely many solutions or no solutions.
Slopes: different
Intersect: one point
Slopes: same
y-intercept: same
Slopes: same
Lines are parallel
The lines are the same
lines don’t intersect
Assignment: pg 367: 10-38 evens
Scales other than 1: 10,12,16?
Writing a system of equations.
Scientists studied the weights of two alligators over a period of 12 months. The
initial weight and growth rate of each alligator are shown below. After how many
months did the alligators weigh the same amount?
Alligator 1
Initial weight: 4 pounds
Rate of growth: 1.5 lb/ month
Alligator 2
Initial weight: 6 pounds
Rate of growth: 1 lb/ month
Initial
Growth rate times Time (t)
weight
Alligator weight (w) = ___________
+ ________________________
Alligator 1:
w = 4 + 1.5t
Alligator 2:
w=6 +1t
Slope = 1.5
Slope = 1
w-intercept = 4
w-intercept = 6
Alligator weights
W
E
I
G
H
T
12
10
8
6
4
2
0
Answer?
4 months
0123456
time
Assignment: pg 367: 10-18,
22-27, skip 15
Scales other than 1: 10,11, 12, 16?