FMa 10 Chapter 7: SYSTEMS OF LINEAR FUNCTIONS
Lesson Notes: 7.5: Using an Elimination
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Strategy to Solve a System of Linear Equations.
LESSON FOCUS: Use the elimination of one variable to solve a linear system.
Make Connections
A carpenter placed two identical plywood sheets end to end and measured their perimeter.
The carpenter placed the sheets side to side and measured their perimeter.
Suppose you wanted to determine the dimensions of a piece of this plywood.
How to set up a linear system that model the situation?
How would you solve the linear system?
In Lesson 7.4, you learned that multiplying or dividing each equation in
a linear system by a non-zero number does not change the solution because
the linear systems that are formed are equivalent. Similarly, adding or subtracting
the two equations in a linear system produces equivalent linear systems. We use
this property to solve a linear system by first eliminating one variable by adding
or subtracting the two equations. This is called solving by elimination.
Example 1) Consider this linear system.
2x + y = –7
x + y = –4
Example 2) Solve this linear system by elimination.
3x – 4y = 7
5x – 6y = 8
CHECK YOUR UNDERSTANDING
Solve this linear system by elimination.
2x + 7y = 24
3x – 2y = –4
Example 3) Solve this linear system by elimination.
CHECK YOUR UNDERSTANDING
Solve this linear system by elimination.
Example 4) a) Write a linear system to model this situation:
An alloy is a mixture of metals. An artist was commissioned to make a
100-g bracelet with a 50% silver alloy. He has a 60% silver alloy and a
35% silver alloy.
b) Solve this problem:
What is the mass of each alloy needed to produce the desired alloy?
CHECK YOUR UNDERSTANDING
a) Write a linear system to model this situation:
An artist was commissioned to make a 625-g statue of a raven with a 40%
silver alloy. She has a 50% silver alloy and a 25% silver alloy.
b) Solve this problem: What is the mass of each alloy needed to produce the
desired statue?
Example 5) Solve this linear system.
2x + 3y = 8
5x – 4y = –6
CHECK YOUR UNDERSTANDING
Solve this linear system.
3x + 9y = 5
9x – 6y = –7