Write down this problem on your
READY RECALL SHEET
Be prepared to explain your answer if you are called on.
Consider the following system of equations.
y = 2x - 4
y = -x - 5
a. Identify the slope and y-intercept of the graph of each equation.
b. Based on your answer for part (a), are the graphs of the two lines
intersecting lines, the same line, or parallel lines? Explain.
find the solution by using the
Elimination method:
Page 92
of your INB
-4x - 15y = -17
-x + 5y = -13
ITEMS of BUSINESS
Questions on Homework?
then Trade-n-Grade
SYSTEMS OF EQUATIONS
11.3 Solving Systems by Elimination
Get into your Groups
find the
solution by using the
Elimination Method:
-4x - 15y = -17
-x + 5y = -13
Page 92-93
of your INB
MATHICAL MAGGIE
Did you know I’m Magic?
Think of 2 numbers
Tell me the Sum and Difference
MATHICAL MATT/MAGGIE
Think of 2 numbers
Tell them the Sum and Difference
How is it done Algebraically?
For any x or y
x + y = SUM
x – y = DIFFERENCE
Ex. x + y = 30
x–y=6
SUM + DIFFERENCE
=
x
2
SUM – x = y
30 + 6
= 18
2
30 – 18 = 12
x = 18
y = 12
I’M USING THE ELIMINATION METHOD!!
ADD THE TWO
EQUATIONS
TOGETHER & SOLVE
x + y = 30
x–y=6
2x = 36
2
2
x = 18
REPLACE x WITH 18
IN ONE OF THE ORIGINAL
EQUATIONS & SOLVE FOR Y
x = 18, y = 12
18 + y = 30
y = 30 - 18
y = 12
(18,12)
Open your
Books
to page
648
.
ELIMINATION METHOD
PG. 648
ELIMINATION METHOD
PG. 648
ELIMINATION METHOD
x = 179 girls; y = 145 boys
PG. 649
LETS TRY A PROBLEM 
Front Page of your homework: A. Guided Practice
1. x - y = 11
2x + y = 19
IS THIS TRUE?
If we have…
Multiply each side by 2, will it still be true?
Multiply each side by -1, or oppositize both
sides. Will it still be true?
Multiply each side by 3, will it still be true?
LETS PRACTICE WITH OUR
COMMUNICATORS
Example: Multiply both sides with 3
x + 2y = 7
A. Multiply both sides with 2
3x - y = 4
B. Multiply both sides with -4
x - 4y = 2
C. Oppositize both sides
x - 3y = -5
3x + 6y = 21
6x - 2y = 8
-4x + 16y = -8
-x + 3y = 5
What would you do to prepare
these equations for elimination?
3𝑥 + 3𝑦 = −21
𝐴.
3𝑥 − 2𝑦 = 14
−4𝑥 − 15𝑦 = −17
B.
−𝑥 + 5𝑦 = −13
−4𝑥 + 9𝑦 = 9
C.
𝑥 − 3𝑦 = −6
ELIMINATION
When using Elimination, we might need to use a
Scaler or to Oppositize in order to eliminate a variable.
Front Page of your homework: A. Guided Practice
2. 7x + 2y = 24
8x + 2y = 30
INB NOTEBOOK ACTIVITY
A. Solve by Elimination:
5x + 2y = 12
-5x + 4y = -66
6y = -54
6
6
y = -9
{
+
5x + 2y = 12
5x + 2(-9) = 12
5x - 18 = 12
+18 +18
5x
= 30
5
5
x =6
Solution:
x, y
(6, -9)
INB NOTEBOOK ACTIVITY
B. Solve by Elimination:
(3x – 5y = -6 ) 3
-9x + 15y = 13
{
9x – 15y = -18
+ -9x + 15y = 13
0 = -5
Is this true?
No!
NO SOLUTION
INB NOTEBOOK ACTIVITY
C. Solve by Elimination:
{
( 2x – 4y = 6 )3
( -3x + 6y = -9)2
6x – 12y = 18
+ -6x + 12y = -18
0 = 0
Is this true?
Yes!
Infinite Solutions
POSSIBLE SOLUTIONS FOR 2 EQUATIONS
(1,3)
Intersecting Lines
Same Slope, y-int. can be
different or the same
Solve Algebraically:
You will get one solution
(X,Y)
Parallel Lines
Coincidental Lines
Same slope, different y-int.
Same line, same slope, same y-int.
Solve Algebraically:
Solve Algebraically:
Variables drop out
FALSE Statement
ex. 12 = 9
Variables drop out
TRUE Statement
ex. 22 = 22
INB NOTEBOOK ACTIVITY
ONE SOLUTION: (X,Y)
ONE SOLUTION: (X,Y)
FALSE STATEMENT
FALSE STATEMENT
TRUE STATEMENT
TRUE STATEMENT
LETS TRY A FEW PROBLEMS
Second Page of your homework: B. Guided Practice
1. 2x - y = 5
2x – y = 7
2. 2x – y = 3
4x - 2y = 6
11.3 Solving Systems by Elimination
find the solution by
using the Elimination method:
-4x - 15y = -17
-x + 5y = -13
Number 14 on your Homework
Write down today’s
homework on your
CALENDAR CARD.
BLUE
Worksheet
11.3
Solving Systems
by Elimination
