Concepts 1.1

1
6/24/2016
Solving Systems by Elimination (opposites)
Objective solve a linear system by elimination
when already having 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
Warm-Up
Solve the system by substitution.
3
Summary
Write a summary about todays lesson.
opposites
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
________.
variable
equations
4
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.
5
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.
6
Notes
Solve the system by linear combination.
1) Arrange the variables.
Ex.
2) Make opposites.
Check
3) Add and solve for the variable.
4) Substitute into ANY original equation.
5) Check your answer.
7
Notes
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.
8
Notes
Solve the system by linear combination.
1) Arrange the variables.
Ex.
2) Make opposites.
Check
3) Add and solve for the variable.
4) Substitute into ANY original equation.
5) Check your answer.
9
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.
10
Notes
Solve the system by linear combination.
1) Arrange the variables.
Ex.
2) Make opposites.
Check
3) Add and solve for the variable.
4) Substitute into ANY original equation.
5) Check your answer.
11
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.
12
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.
13
Class Work
Solve the system by linear combination.
14
Todays Homework
p414 8-15
Rules for Homework

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