Download Jan. 6

Solve the system:
3x + y = 1
y = x + 9
When finished, place your paper in
the red tray and pick notes for today.
1
2
Chapter 3--Section 2, Part 2
Elimination
Objective: To solve linear systems using the elimination method.
Steps to follow for the elimination method:
1.
Using multiplication, make one variable have the
opposite coefficients.
2.
Omit the variable from Step 1 by adding the two
equations together.
3.
From the remaining portion of Step 2, solve for the
variable that is left.
4.
Substitute the answer from Step 3 into one of the
original equations to solve for the missing variable.
3
Steps to follow for the elimination method:
Example 1:
3x + 2y = 4
4x - 2y = -18
1.
Using multiplication, make one variable have the
opposite coefficients.
2.
Omit the variable from Step 1 by adding the two
equations together.
3.
From the remaining portion of Step 2, solve for the
variable that is left.
4.
Substitute the answer from Step 3 into one of the
original equations to solve for the missing variable.
4
Steps to follow for the elimination method:
Example 3:
3x + 5y = -16
2x + 3y = -9
1.
Using multiplication, make one variable have the
opposite coefficients.
2.
Omit the variable from Step 1 by adding the two
equations together.
3.
From the remaining portion of Step 2, solve for the
variable that is left.
4.
Substitute the answer from Step 3 into one of the
original equations to solve for the missing variable.
5
Steps to follow for the elimination method:
Example 2:
-4x + 7y = 2
4x - 5y = 10
1.
Using multiplication, make one variable have the
opposite coefficients.
2.
Omit the variable from Step 1 by adding the two
equations together.
3.
From the remaining portion of Step 2, solve for the
variable that is left.
4.
Substitute the answer from Step 3 into one of the
original equations to solve for the missing variable.
6
Example 4:
2x - y = 13
3x + 4y = 3
Steps to follow for the elimination method:
1.
Using multiplication, make one variable have the
opposite coefficients.
2.
Omit the variable from Step 1 by adding the two
equations together.
3.
From the remaining portion of Step 2, solve for the
variable that is left.
4.
Substitute the answer from Step 3 into one of the
original equations to solve for the missing variable.
7
NOTE:
If a solution to an elimination problem is...
1 = 5 0 = 0
(or two other numbers)
..........then there are INFINITE number of solutions to the system. In other words, the equations are representing the SAME line.
..........then there are NO solutions to the system. In other words, the equations are representing the PARALLEL line.
6 = 6 (or other equal numbers)
..........then there is ONE solution to the system. In other words, the equations are representing the INTERSECTING line.
8
Ho
m
ew
or
k
Chapter 3--Section 2
Linear Equations
194
problems: 6-13, 19-26
9