10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
Warm-up:
Graph these two equations to find their intersection.
1 x + 1
y = 2
3
y = x ­ 1
2
Intersection:
(2, 2)
Answer is hiding!
Jul 31­1:44 PM
1
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
10.1 Systems of Linear Equations: Substitution and Elimination Day 1
Objectives :
1. Express the solution of a system of dependent equations containing two variables.
2. Identify inconsistent systems of equations containing two variables.
3. Solve systems of equations by substituting.
4. Solve systems of equations by elimination.
Nov 9­12:04 PM
2
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
System of Equations:
Two or more equations that use the same variables.
1 x + 1
y = 2
What values of x and y will
satisfy BOTH of these
equations?
3 x ­ 1
y = How do we figure it out?
2
Graph both equations!
Jul 31­1:41 PM
3
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
What is the solution to this system of equations?
y = x + 3
1 x
y = ­ 2
Solution:
(­2, 1)
Jul 31­1:47 PM
4
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
Types of Linear Systems
One Solution
Intersecting Lines
No Solution
Parallel Lines
y = 3x ­ 4
y = ­x + 2
y = x ­ 3
y = x + 1
System is consistent and equations are independent.
System is inconsistent.
Many Solutions
Same Line
y = ­x ­ 4
2x + 2y = ­8 System is consistent and equations are dependent.
Jul 31­1:50 PM
5
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
Use this system of equations:
4x ­ y = 2
3y = 12x ­ 6
A) Without graphing, describe the
relationship between the graphs of the
equations.
B) Tell whether the
system of equations has
one solution,
no solutions, or
many solutions.
C) Identify the system as
consistent/independent,
inconsistent, or
consistent/dependent.
Jul 31­1:54 PM
6
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
Use this system of equations:
3x + 2y = ­6
5x ­ 2y = ­10
A) Without graphing, describe the
relationship between the graphs of the
equations.
B) Tell whether the
system of equations has
one solution,
no solutions, or
many solutions.
C) Identify the system as
consistent/independent,
inconsistent, or
consistent/dependent.
Jul 31­1:54 PM
7
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
Solving by
Substitution
Nov 28­10:54 AM
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10.1 Day 1 Systems of Linear Equations 2010
Solve this system of equations by substitution.
November 29, 2010
2x ­ 4y = ­22
x + y = 4
Step 1: Solve either equation for one of its variables.
Step 2: Substitute into the other equation.
Step 3: Solve for the variable.
Steps 4 & 5
Nov 26­4:28 PM
9
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
2x ­ 4y = ­22
x + y = 4
Step 4: Find the other variable by back­substitution.
Step 5: State your results and check your answer.
(­1, 5)
Nov 26­5:34 PM
10
10.1 Day 1 Systems of Linear Equations 2010
Solve this system of equations by substitution.
November 29, 2010
x + y = 272
7x + 4y = 1694
x = 202
y = 70
Nov 26­5:40 PM
11
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
So...what is elimination?
Elimination is getting rid of one of the
variables by adding both sets of equations.
Let's Try One!
Snowman scene
12
10.1 Day 1 Systems of Linear Equations 2010
Solve this system of equations by elimination.
November 29, 2010
3y = 2x + 2
2 ­ x = ­3y
Step 1: Move all variables to the left side and write them in the same order.
Step 2: Choose one set of variables to eliminate. Make the coefficients opposite of each other.
Step 3: Draw a line under the equations and add them together.
Steps 4, 5 & 6
Oct 1­11:04 AM
13
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
3y = 2x + 2
2 ­ x = ­3y
Step 4: Solve for the remaining variable.
Step 5: Find the other variable by back­substitution.
Step 6: State your results and check your answer.
Oct 1­11:04 AM
14
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
Solve this system of equations by elimination.
4x ­ 3y = 11
­5x +2y = ­12
(2, ­1)
Oct 1­11:04 AM
15
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
Solve this system of equations by elimination.
2x ­ 9y = ­35
6x + 7y = 65
(5, 5)
Oct 1­11:04 AM
16
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
Last but not least:
The perimeter of a rectangular floor is 90 feet. Find the dimensions of the floor if the length is twice the width.
Nov 28­11:39 AM
17
10.1 Day 1 Systems of Linear Equations 2010
November 29, 2010
Homework
page 737 (3 ­ 8, 18 ­ 30 even, 56 ­ 58, 63) Outdoor scene
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