Title:  Elimination Using Addition and Subtraction
Grade:  9th
Section:  7.3 

Materials:  calculators, worksheets, chalkboard/whiteboard, chalk/markers
**ALL WORKSHEETS WILL BE PROVIDED

Lesson Overview:  Students will learn how to solve system of equations by using elimination with addition and subtraction.  They will also be able to write a system of equations.

Lesson Objectives:  
•	Students will be able to write a systems of equations, and identify was they are trying to solve for.  [Application]
•	Students will analyze and solve problems whose solution requires solving systems of linear equations in two variables, either by addition or subtraction.  [Analysis]
•	Given a word problem the students will be able to create a system of equations from the information, solve through elimination (addition/subtraction), and then evaluate the appropriateness of their answer.  [Evaluation]

NYS Standards:
•	Key Idea 3: Operations- Use addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions.
•	Key Idea 4:  Modeling/Multiple Representation- Model real-world problems with systems of equations and inequalities.
•	Key Idea 7:  Patterns/Functions- Represent and analyze functions, using verbal descriptions and equations.

Anticipatory Set: (5 mins)
Pass out “What’s Wrong With These Answers?” worksheet.  Students should work with a partner to complete this, and then go over as a class.  This will be a brief review of writing equations as well as how to solve them.  Each problem is followed by an answer that has something wrong in it.  The student should circle the error and then rewrite the answer correctly.

Developmental Activity: (25 mins)
1.)	Pass out “Solving Systems of Equations with Elimination (Addition and Subtraction)” worksheet.
2.)	Briefly review what a system of equations is.  (Students were introduced to them and how to graph them in the previous lesson.)
3.)	Complete the worksheet as a whole group.
4.)	The examples are broken up into steps, with questions to help guide the students thought process.  Be sure to discuss the students’ responses.

Closure: (5 mins)
Discuss what they learned about elimination.  When do you use addition?  When do you use subtraction?  How do you find the second variable?  These are just a few suggestions.

Assessment: (5 mins)
Have the students complete the Exit Ticket and hand it in before they leave.  This will be graded.

Name:										Date:

What’s Wrong With These Answers?

Directions:  Each of the following problems has an answer that is INCORRECT.  It is your job to find and circle the error that the student made.  Then answer the question correctly.

1.)  A rectangular garden has a width that is 10 feet less than twice the length.  Write an equation to find the dimensions if the perimeter is 50 feet.

	Answer:  L= length
		    (2L + 10) + L = 50

	What is wrong with the equation?

	Correct Equation:

2.)  Solve the following equations for x:

	5x + 15 = 60
	     +15   +15
	        5x = 75
          x = 12 
	
Correct Response with Proper Work Shown:

	2x + 12 = 3x – 5
	        -5            -5
	2x + 7 = 3x
           -2x	  -2x
	        7 = x

Correct Response with Proper Work Shown:

Name:	ANSWER KEY								Date:

What’s Wrong With These Answers?

Directions:  Each of the following problems has an answer that is INCORRECT.  It is your job to find and circle the error that the student made.  Then answer the question correctly.

1.)  A rectangular garden has a width that is 10 feet less than twice the length.  Write an equation to find the dimensions if the perimeter is 50 feet.

	Answer:  L= length
		    (2L + 10) + L = 50

	What is wrong with the equation?
		+ 10 SHOULD BE -10

	Correct Equation:
		(2L - 10) + L = 50

2.)  Solve the following equations for x:

	5x + 15 = 60
	     +15   +15
	        5x = 75
          x = 12 
	
Correct Response with Proper Work Shown:
	SUBTRACT 15 ON BOTH SIDES
		X = 9

	2x + 12 = 3x – 5
	        -5            -5
	2x + 7 = 3x
           -2x	  -2x
	        7 = x

Correct Response with Proper Work Shown:
	ADD 5 TO BOTH SIDES
		X= 17

Name:										Date:

Solving Systems of Equations with Elimination
(Addition and Subtraction)

On the winter solstice, there are a few hours of daylight in the Northern Hemisphere than on any other day.  On that day in Seward, Alaska, the difference between the number of hours of darkness n and the number of hours of daylight d is 12.  This situation is represented by the following system of equations.
n + d = 24
n – d = 12

What do you notice about these two equations? _________________________

Sometimes adding two equations together will eliminate one variable.  Using this step to solve a system of equations is called _____________________.

1.)  Use elimination to solve each system of equations.
		x – 2y = 13
	          3x + 2y = 15

What do you notice about the coefficients of the y-terms? ______________________

How will you be able to “eliminate” the y-terms? ____________________________

Now, solve for x:

How will we get our y-value?  ________________________________________

Solve for y:

The solution of the system is? __________________
Check answer:

We know that a variable can be eliminated with addition if the coefficients are the same but the signs are opposite.  What if the coefficients and the signs are the same?
We can eliminate the variable by ________________ the two equations.  

2.) Use elimination to solve each system of equations.
	3x + 4y = 5
	3x  – y = -5 

What do you notice about the coefficients of the x-terms? ______________________

How will you be able to “eliminate” the x-terms? ____________________________

Now, solve for y:

How will we get our x-value?  ________________________________________

Solve for x:

The solution of the system is? __________________
Check Answer:

3.)  A can of pop and a bag of chips together cost $2.05.  Two cans of pop and a bag of chips cost $2.70.  How much does a single can of pop cost?

Name:	ANSWER KEY								Date:

Solving Systems of Equations with Elimination
(Addition and Subtraction)

On the winter solstice, there are a few hours of daylight in the Northern Hemisphere than on any other day.  On that day in Seward, Alaska, the difference between the number of hours of darkness n and the number of hours of daylight d is 12.  This situation is represented by the following system of equations.
n + d = 24
n – d = 12

What do you notice about these two equations? IF THE 2 EQUATIONS ARE ADDED THE d VARIABLE WILL DISAPPEAR, BECAUSE THEY HAVE DIFFERENT SIGNS.

Sometimes adding two equations together will eliminate one variable.  Using this step to solve a system of equations is called ELIMINATION.

1.)  Use elimination to solve each system of equations.
		x – 2y = 13
	          3x + 2y = 15

What do you notice about the coefficients of the y-terms? THEY ARE THE SAME NUMBER WITH DIFFERENT SIGNS.

How will you be able to “eliminate” the y-terms? ADD THE EQUATIONS

Now, solve for x:

How will we get our y-value? PLUG IN 7 FOR X INTO ONE OF THE EQUATIONS

Solve for y:

The solution of the system is? (7, -3)
Check Answer:  7-2(-3) = 13
		3(7) +2(-3) =15
We know that a variable can be eliminated with addition if the coefficients are the same but the signs are opposite.  What if the coefficients and the signs are the same?
We can eliminate the variable by SUBTRACTING the two equations.  

2.) Use elimination to solve each system of equations.
	3x + 4y = 5
	3x  – y = -5 

What do you notice about the coefficients of the x-terms? THEY ARE THE SAME AND HAVE THE SAME SIGN

How will you be able to “eliminate” the x-terms? SUBTRACT THE EQUATIONS
Now, solve for y:

	Y =2

How will we get our x-value?  Plug 2 into an equation for y.

Solve for x:
3x+4(2)=5
x = -1

The solution of the system is? (2, -1)
Check Answer:  3(-1)+4(2)=5	         3(-1) – (2)= -5

3.)  A can of pop and a bag of chips together cost $2.05.  Two cans of pop and a bag of chips cost $2.70.  How much does a single can of pop cost?

X= can of pop
Y = bag of chips

    2X + Y = $2.70
(-)  X + Y=  $2.05
             X = $.65
$.65 + Y = $2.05
           Y = $1.40
2(.65) +1.40= $2.70
.65 + 1.40 = $2.05

Name:										Date:

Exit Ticket

Directions:  Set up the system of equations, and solve.  Be sure to check your answer.  Show all work!

1.)  Find the two numbers whose sum is 51 and whose difference is 13.

Name:	ANSWER KEY								Date:

Exit Ticket

Directions:  Set up the system of equations, and solve.  Be sure to check your answer.  Show all work!

1.)  Find the two numbers whose sum is 51 and whose difference is 13.

		x + y = 51
		x – y = 13

		2x = 64
		  x = 32
	
		32 + y = 51
		        y = 19

		32 + 19 = 51
		32 – 19 = 13