Download Section 7 * 1 Solving Systems of Equations by Graphing

Section 7 – 1
Solving Systems of Equations
by
Graphing
Objectives:
To solve systems by graphing
To analyze special types of systems
System of Linear Equations:
Two or more linear equations
Example:
y = 2x – 3
y=x–1
2x + 3y = 12
y = 6x + 2
There are Three Ways to Solve a System of Linear Equations:
1) Graphing
2) Substitution
3) Elimination
Solution of the System of Linear Equations:
A point (ordered pair) that both lines have in
common when they are graphed.
This ordered pair will make ALL the equations
true when it is plugged in.
Is (-1, 5) a solution to the system?
Is (3, -2) a solution to the system?
x+y=4
6x – 6y = 2
x = -1
3x + 9y = -7
Example 1
Solving a System by Graphing
A) Solve by graphing.
y = 2x – 3
y=x–1
CHECK YOUR ANSWER:
B)
Solve by graphing.
y=x+5
y = -4x
CHECK YOUR ANSWER:
C)
Solve by graphing.
𝑦=
1
− 𝑥
2
+2
𝑦 = −3𝑥 − 3
CHECK YOUR ANSWER:
D)
Solve by graphing.
2y – 4x = 2
2y – 6x = -2
CHECK YOUR ANSWER:
Homework:
Textbook Page 343; # 2 – 12 Even
(Make sure to Check ALL answers!)
Section 7 – 1
Continued…
Objectives:
To solve systems by graphing
To analyze special types of systems
Example 2
Word Problems
A)
Suppose you plan to start taking a kick-boxing
class. Nonmembers pay $4 per class and members pay
a $10 fee plus an additional $2 per class. After how
many classes will the cost be the same? What is that
cost?
B)
Suppose you are testing two fertilizers on
bamboo plants A and B, which are growing under
identical conditions. Plant A is 6 cm tall and growing at
a rate of 4cm/day. Plant B is 10 cm tall and growing at a
rate of 2cm/day. After how many days will the bamboo
plants be the same height? What will their height be?
C)
Suppose you have $20 in your bank account. You start
saving $5 each week. Your friend has $5 in his account and is
saving $10 each week. Assume that neither you nor your friend
makes any withdrawals. After how many weeks will you and your
friend have the same amount of money in your accounts? How
much money will each of you have?
Homework:
Complete Word Problem Worksheet