EOC Systems of equations Solve each system by graphing. 3 ...
Warm-up Solve the first system of equations by the Substitution Method, then graphing.
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Transcript of Warm-up Solve the first system of equations by the Substitution Method, then graphing.
Warm-up• Solve the first system of equations by the
Substitution Method, then graphing
3 16
2 3 4
x y
x y
(4, 4)
1. (6, 1)
2. (4,4)
3. (2,1)
4 24. ( , )
3 3
6. ( 10,6)
5. No Solution
7. : $450 : $100
4
50 20 550
E A
E A
E A
8. 4 5
9
479 339 3611
Electric Acoustic
E A
E A
Solving Linear Systems Algebraically with Elimination
Section 3-2
Pages 160-1-67
Objectives
• I can use the elimination method to solve equations
• I can set up and solve word problems using elimination
Elimination Method
• GOAL
• 1. Add the equations together and have one variable term go away.
• 2. Sometimes you will have to multiply one or both equations by a number to make this happen.
Example 1
3 2 6
4 2 8
x y
x y
7 14x
2x Now, PLUG this back intoEither equation to find “y”
3(2) 2 6y
6 2 6y 2 0y
0y
(2,0)
What does this mean?
• Remember that a solution to a system of equations is where the graphs cross
• It is ALWAYS an Ordered Pair
Multiplying by a number?
• Many times you cannot add the equations and have a variable term cancel
• For these cases, you must multiply One or Both equations by a number first
• Let’s look at a few
What to Multiply by?45
932
yx
yx
)45(2
)932(5
yx
yx
)45(3
)932(
yx
yx
x-variable will cancel
y-variable will cancel
Example 23 5 4
2 3 29
x y
x y
2(3 5 4)
3(2 3 29)
x y
x y
6 10 8
6 9 87
x y
x y
19 95y
5y
2 3( 5) 29x
2 15 29x
2 14x
7x
(7, 5)
Your Turn
• Solve the following system of equations using elimination:
2932
1127
yx
yx)9,1(: Solution
Other Methods
• Remember, the solution to a system of equations if an ordered pair
• You know 2 other methods to check your answers:– Graphing Calculator and asking for the
intersection (2nd, Trace, Intersection, E, E, E)– Substitution Method
Solution Types
Remember there are 3 types of solutions possible from a system of equations!
No Solution vs Infinite
• How will you know if you have No Solution or Infinite Solutions when solving by Substitution??
Remember Back to Solving Equations
No Solution• Variables are gone and
you get this:
• 2x + 3 = 2x – 4• 3 = -4• This is not possible, so
• No Solution
Infinite Solutions• Variables are gone and
you get this:
• 2x + 3 = 2x + 3• 3 = 3• This is always true, so
• Infinite Solutions
Word Problems
• When solving a word problem, consider these suggestions
• 1. Identify what the two variables are in the problem
• 2. Write equations that would represent the word problem, looking for key words
• Sum, difference, twice, product, half, etc…
Example 1
• GEOMETRY: The length of a rectangle is 8 cm more than twice the width. If the perimeter is 40 cm, find the dimensions.
Variables:
Length (L)
Width (W)
Equations:
L = 2W + 8
2L + 2W = P
Now, solve by elimination
Example 2
• Rental car agency A charges $8 per day plus $.20 per mile. Rental car company B charges $10, but only $.10 per mile. At what mileage is it better to use Company B?
Cost (C)
Miles (M)
Equations:
C = 8 + .20M
C = 10 + .10M
Now, solve by Elimination
Homework
• Elimination Worksheet