consider the following system of equations . y = 2x - 4 y = -x - 5
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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 Identify the slope and y-intercept of the graph of each equation . - PowerPoint PPT PresentationTRANSCRIPT
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.
i-can
Page 92 of your INB
Write down this problem on yourREADY RECALL SHEET
Be prepared to explain your answer if you are called on.
find the solution by using the Elimination method:
-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
i-canGet into your Groups
Page 92-93 of your INB
find the solution by using the Elimination Method:
-4x - 15y = -17 -x + 5y = -13
MATHICAL MAGGIE
Did you know I’m Magic?
I can read your mind
Think of 2 numbersTell me the Sum and Difference
MATHICAL MATT/MAGGIE
ARE YOUMAGICAL NOW?Show your Partner
Think of 2 numbersTell them the Sum and Difference
How is it done Algebraically?
For any x or yx + y = SUM
x – y = DIFFERENCE
SUM + DIFFERENCE2 = x
SUM – x = yEx. x + y = 30 x – y = 6
30 + 62 = 18 30 – 18 = 12 x = 18
y = 12I’M USING THE ELIMINATION METHOD!!
x + y = 30x – y = 6 ADD THE TWO
EQUATIONS TOGETHER & SOLVE
2x = 362 2x = 18
REPLACE x WITH 18IN ONE OF THE ORIGINAL
EQUATIONS & SOLVE FOR Y
18 + y = 30y = 30 - 18y = 12
x = 18, y = 12 (18,12)
Open your Books
to page 648.
ELIMINATION METHODPG. 648
ELIMINATION METHODPG. 648
ELIMINATION METHOD PG. 649
x = 179 girls; y = 145 boys
LETS TRY A PROBLEM
1. x - y = 11 2x + y = 19
Front Page of your homework: A. Guided Practice
IS THIS TRUE?If we
have… y = 4
2(y) = 2(4)2y =
8y = 4
Multiply each side by 2, will it still be true?
3(y) = 3(4)3y = 12y = 4
Multiply each side by 3, will it still be true?
-1(y) = -1(4)-1y = -
4y = 4
Multiply each side by -1, or oppositize both sides. Will it still be true? Sooo…
Is each equation still
true if we Multiply each side with a
Scaleror Oppositize
them?
LETS PRACTICE WITH OUR COMMUNICATORS
Example: Multiply both sides with 3 x + 2y = 7 3x + 6y = 21
A. Multiply both sides with 2 3x - y = 4 6x - 2y = 8B. Multiply both sides with -4 x - 4y = 2 -4x + 16y = -8
C. Oppositize both sides x - 3y = -5 -x + 3y = 5
What would you do to prepare these equations for
elimination?
𝐴 .3 𝑥+3 𝑦=−213 𝑥−2 𝑦=14
B.
C .−4 𝑥+9 𝑦=9𝑥−3 𝑦=−6
ELIMINATIONWhen 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
A. Solve by Elimination:{ 5x + 2y = 12
-5x + 4y = -66+ 6y = -54 6 6y = -9
5x + 2y = 12 5x + 2(-9) = 12
5x - 18 = 12+18 +18
5x = 305 5
x = 6
INB
NOTE
BOOK
AC
TIVI
TY
Solution: (6, -9)
x, y
B. Solve by Elimination:
– 15y
{ 3x – 5y = -6 -9x + 15y = 13
9x-9x + 15y = 13+
0 = -5Is this true?
( ) 3
= -18
No!INB
NOTE
BOOK
AC
TIVI
TY
NO SOLUTION
C. Solve by Elimination:
Is this true?Yes!
– 12y
{ 2x – 4y = 6
-3x + 6y = -9 6x -6x+
0 = 0
( )3
= 18
( )2
+ 12y = -18
INB
NOTE
BOOK
AC
TIVI
TY
Infinite Solutions
POSSIBLE SOLUTIONS FOR 2 EQUATIONS
One Solution No SolutionInfinitely
Many Solutions
(1,3)
Intersecting LinesSame Slope, y-int. can be
different or the same
Solve Algebraically: You will get one solution
(X,Y)
Parallel LinesSame slope, different y-int.
Solve Algebraically: Variables drop out FALSE Statement
ex. 12 = 9
Coincidental LinesSame line, same slope, same y-int.
Solve Algebraically: 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
1. 2x - y = 5 2x – y = 7
Second Page of your homework: B. Guided Practice
2. 2x – y = 3 4x - 2y = 6
i-can find the solution byusing the Elimination method:
Number 14 on your Homework
11.3 Solving Systems by Elimination
-4x - 15y = -17 -x + 5y = -13
Write down today’s homework on yourCALENDAR CARD.
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11.3 Solving Systemsby Elimination