Concepts 1.1

1
Algebra 1
6/24/2016
Solving Systems by Elimination (multiply)
Objective solve a linear system by elimination
when first having to make opposites.
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.
2
Yesterdays Homework

• Any questions?
• 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.

3
Introduction
To solve a linear system using __________ first
multiply one or both of the equations to make
_________. Now add up your two _________ and
solve for the remaining variable. Plug that
solution back into any equation to find the other
________.
elimination
opposites
equations
variable
4
Warm-Up
Solve the system by linear combination.
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Notes

• Solving a System by Linear Combination

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.
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When solving a system of two linear equations in
two variables1. If an identity is obtained,
such as 0 0, then the system has an infinite
number of solutions are dependent and, since a
solution exists, the system is consistent. 2.
If a contradiction is obtained, such as 0 7,
then the system has no solution. The system is
inconsistent.
Rules for Special Cases
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Notes
Solve the system by linear combination.
1) Arrange the variables.
Ex.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
5) Check your answer.
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Notes
Now you try.
Solve the system by linear combination.
1) Arrange the variables.
Ex.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
5) Check your answer.
9
Notes
Solve the system by linear combination.
1) Arrange the variables.
Ex.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
5) Check your answer.
10
Notes
Solve the system by linear combination.
1) Arrange the variables.
Ex.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
5) Check your answer.
11
Notes
Now you try.
1) Arrange the variables.
Solve the system by linear combination.
Ex.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
5) Check your answer.
12
Notes
Now you try.
Solve the system by linear combination.
1) Arrange the variables.
Ex.
2) Make opposites.
3) Add and solve for the variable.
4) Substitute into ANY original equation.
5) Check your answer.
13
Class Work
Solve the system by linear combination.
14
Ticket Out the Door
Complete the Ticket Out the Door without
talking!!!!!
Talking time after the bell!
Put your NAME on the paper.
When finished, turn your paper face DOWN.
Solve the system.
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Todays Homework
NO Homework!!!!!
Rules for Homework

• Pencil ONLY.
• Must show all of your work.
• NO WORK NO CREDIT
• Must attempt EVERY problem.
• Always check your answers.