2016­11­18 systems elimination .notebook
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Textbook Section 5.3
pg. 251 #3-21 odd
HW Answers
November 18, 2016
2016­11­18 systems elimination .notebook
November 18, 2016
Today's Objective: Solving linear systems
Elimination Method
2016­11­18 systems elimination .notebook
November 18, 2016
Solving Systems Method #2
Elimination
We can use our knowledge of additive inverses to help solve systems of equations. What happens if I add these equations to each other?
2x + 3y = 11
­2x + 5y = 13
Elimination Method to Solve Systems
1. Check for inverses. If there aren't any, multiply one or both
equations by a constant to create them.
2. Add vertically to eliminate a variable, solve for the remaining
variable. **It helps to line up the equations in the same order**
3. Substitute that value into one of the equations and solve for the
other variable.
4. Check solution in other equation
2016­11­18 systems elimination .notebook
November 18, 2016
Solve each system
­4x ­ 2y = ­12
4x + 8y = ­24
­2x + 7y = 5
3x ­ 7y = ­4
Solving a system by creating an equivalent system
Choose a multiple that will eliminate a variable when the two equations are added together. Original System
2x + y = 6
x - 3y = -11
New System
Solution
2016­11­18 systems elimination .notebook
November 18, 2016
Choose a multiple that will eliminate a variable when the two equations are added together. Original System
New System
Challenge
Solve the following system
Solution
2016­11­18 systems elimination .notebook
November 18, 2016
Practice
Solve the system of linear equations by elimination. Check your solution.
1. 3x + 2y = 7 2. x − 3y = 24 3. x + 4y = 22
−3x + 4y = 5 3x + y = 12 4x + y = 13
A business with two locations buys seven large delivery vans and five small delivery vans. Location A receives five large vans and two small vans for a total cost of $235,000. Location B receives two large vans and three small vans for a total cost of $160,000. What is the cost of each type of van?
2016­11­18 systems elimination .notebook
November 18, 2016