Download Solve systems of linear equations using the elimination method

Solve Systems of Linear
Equations with a
Common Term Using
the Elimination Method
Learning Target
I CAN solve systems
of linear equations
using the elimination
method.
Previous Lesson
In the previous lesson, you learned
how to solve systems of linear
equations by using tables of values.
You may have noticed that it is not
always easy to find the solution, so
you need to adopt a more
systematic approach.
Algebraic Approach
Consider the system of
linear equations below:
5s + 2t = 6— Equation 1
9s + 2t = 22— Equation 2
Start Thinking About
Elimination
• Both equations have 2t term.
• If you subtract the two equations,
you will have one equation with
only one variable s.
ELIMINATION METHOD
Subtract Equation 2 from Equation 1:
5s + 2t = 6
- 9s + 2t = 22
- 4s
= - 16
-4
- 4 -- Divide both sides by – 4.
s=4
ELIMINATION METHOD
Substitute s = 4 into Equation 1:
5(4) + 2t = 6
20 + 2t = 6
- 20
- 20 --- Subtract 20.
2t = - 14
2
2 --- Divide both sides by 2.
t=-7
So the solution of the system of equations is s = 4, t = 7, or (4, - 7)    
ELIMINATION METHOD Summary
By adding or subtracting two
equations with a common term,
you get an equation with only one
variable. This method of solving
systems of equations is known as
the ELIMINATION METHOD.
 Your Turn 
Solve by using the
elimination method, the
system of linear equations.
4x + y = 9
3x - y = 5
 Your Turn 
Add Equation 1 and Equation 2.
4x + y = 9
+ 3x - y = 5
7x = 14
7
7 ---- Divide both sides by 7.
x=2
 Your Turn 
Substitute x = 2 into the second equation.
3(2) – y = 5
6–y=5
-6
- 6 ---- Subtract 6 from both sides
-y=-1
- 1 - 1 --- Divide both sides by – 1
y=1
The solution to this system of equations is (2, 1).
Assignment
• First, copy down problems #4 – 29 and the
directions on page 385 in the red algebra I
book.
• After successfully copying down problems #4 29 and the directions on page 385, start
solving each system of equations.
• Remember to show all of your work.
• Remember, I can take up any assignment and
count it as a take-home quiz grade at any
time.