Copyright 2012 by www.rsquaredcreation.com. All rights reserved. If you have any questions please contact [email protected]. The work in this PowerPoint is the property of r squared creation. The copying or distribution of this work is ILLEGAL, including but not limited to the posting of the PowerPoint online. Teachers are not exempt in any way, shape, or form. To avoid copyright infringement written permission from the creator is necessary. r creation 2 WARNING
Transcript
Copyright 2012 by www.rsquaredcreation.com. All rights reserved.If you have any questions please contact [email protected].
The work in this PowerPoint is the property of r squared creation. The copying or distribution of this work is ILLEGAL, including
but not limited to the posting of the PowerPoint online. Teachers are not exempt in any way, shape, or form.
To avoid copyright infringement written permission from the creator is necessary.
rcreation
2
WARNING
Before We Get StartedREMEMBER TO ALWAYS BE RESPECTFUL!
"Wise men speak because they have something to say; fools because they have to say something.” - Plato
NO food or drinks are allowed.• Please put your gum into the trash.
NO electronics are allowed.• Please put away cell phones and music players.
Yesterday’s Homework
1. Any questions?2. Please pass your homework to the front.
• Make sure the correct heading is on your paper.• Is your NAME on your paper?
• Make sure the homework is 100% complete.• Incomplete work will NOT be accepted.
What Do Notes Look Like?• Heading
• Date
• Section # and Title
• IWBAT (I will be able to)
• Warm-Up
• Notes• You do not have to copy the text in blue!
• Class Work
• Summary
Solving Systems by Elimination (opposites)
04/19/23
Heading
IWBAT: solve a linear system by elimination when already having opposites. (CA St. 9)
Standard 9: Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
6.3A
Warm-Up
31.
2 4 6
x
x y
Solve the system by substitution.
2 4 6x y 2 4 6y 3
6 6
3y
3, 3
6 4 6y
4 44 12y
22.
3 4 10
y x
x y
3 4 10x y 3 4 10x 2x
2x 2, 4
3 8 10x x
5 55 10x
2y x 2y 2
4y
Notes• Solving a System by Elimination
1. Arrange the like variables in columns.
- This is already done.
2. Pick a variable, x or y, and make the two equations opposites using multiplication.
3. Add the equations together (eliminating a variable) and solve for the remaining variable.
4. Substitute the answer into one of the ORIGINAL equations and solve.
5. Check your solution.
Notes
2 5
2 3 7
x y
x y
Ex.
Solve the system by linear combination.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
1) Arrange the variables.
3y
1, 35) Check your answer.
4 12y 4 4
2 5x y 2 5x 3
3 3 2 2x 2 2
1x
Notes
2 5
2 3 7
x y
x y
Ex.
Solve the system by linear combination.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
1) Arrange the variables.
5) Check your answer.
2 5x y 2 5 1 3
2 3 5
Check
5 5
2 3 7x y 2 3 7 1 3
2 9 7 7 7
1, 3
Notes
5 4 6
3 4 2
x y
x y
Ex.
Solve the system by linear combination.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
1) Arrange the variables.
2x
2, 1 5) Check your answer.
2 4x 2 2
5 4 6x y 5 4 6y 2
10 10 4 4y 4 4
1y
10 4 6y
Now you try.
Notes
5 4 6
3 4 2
x y
x y
Ex.
Solve the system by linear combination.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
1) Arrange the variables.
5) Check your answer.
5 4 6x y 5 4 6 2 1
10 4 6
Check
6 6
3 4 2x y 3 4 2 2 1
6 4 2 2 2
2, 1
Notes
3 5 2
3 6 6
x y
x y
Ex.
Solve the system by linear combination.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
1) Arrange the variables.
4y
6, 4 5) Check your answer.
1 4y 1 1
3 5 2x y 3 5 2x 4
20 20 3 18x 3 3
6x
3 20 2x
Now you try.
Notes
Ex.
Solve the system by linear combination.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
1) Arrange the variables.
5) Check your answer.
3 5 2x y 3 5 2 6 4
18 20 2
Check
2 2
3 6 6x y 3 6 6 6 4
18 24 6 6 6
3 5 2
3 6 6
x y
x y
6, 4
Notes
6 7 10
6 7 10
x y
x y
Ex.
Solve the system by linear combination.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
1) Arrange the variables.
Infinite Solutions
5) Check your answer.
0 0
Notes
5 8 9
5 8 2
x y
x y
Ex.
Solve the system by linear combination.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
1) Arrange the variables.
No Solution
5) Check your answer.
0 11
Now you try.
Class Work
2 5 21.
2 3 18
x y
x y
6, 2
Solve the system by linear combination.
4 12.
2
x y
x y
3, 1
4 3 73.
4 2 2
x y
x y
1, 1 2 5
4.3 2 11
x y
x y
3, 1
5 6 45.
2 6 2
x y
x y
2, 1
3 146.
2 1
x y
x y
3, 56 2 2
7.6 2 4
x y
x y
No Solution
3 138.
4 16
x y
x y
3, 4
5 4 139.
5 4 13
x y
x y
Infinite Solutions
3 710.
1
x y
x y
4, 5
2 2 1811.
2 9
x y
x y
6, 3
5 2 1612.
2 8
x y
x y
4, 2
Summary
Write a summary about today’s lesson.
When a linear system already has ________ just add up both equations and solve for one of the variables. Next plug that solution back into any of the original _________ to find the other ________.
opposites
equations variable
Worksheet 6.3A
Today’s Homework
1. Pencil ONLY.2. Must show all of your work.
• NO WORK = NO CREDIT3. Must attempt EVERY problem.4. Always check your answers.
Rules for Homework
Complete the Ticket Out the Door without talking!!!!!
