System of L.E.: Elimination
Breakthrough Denver
GETTING YOURSELF READY
Materials:
Your Preparation:
Homework (if needed get from
Brooke)
Create In class problems
Create VIP.
Agenda (w/times):
Review Homework (10-15mins)
Do Now (3mins)
Teaching (25mins-30mins)
Guided Practice
Closure (3mins)
GETTING YOUR STUDENTS READY
*Do Now: Present 5 systems of equations on whiteboard. Have students identify the opposite terms.
2x-5y = -20
x+7y=13
2x-3y= 8
2a+b= 6
4m+3n=13
4x+5y= 14
x-7y= 5
5x+3y= 20
-2a-3b= 8
2n-4m= 1
“What happens when we add up opposite terms? We get zero!!!. This is the fact we will be using to solve for x
and y, using opposite terms. Using this opposite terms is called Elimination.
Objective: Today you will be able to…
Find the point of intersection of two lines
Proving behavior: by…
Solving system of linear equations using elimination.
Purpose: We are doing this because…
Algebra skills for high school.
TEACHING
Step 1:
Say: So let’s find the point of intersection of these two lines by using elimination. The first
Identify Opposite step is to identify the opposite terms. What terms can we eliminate?
Terms
See: 3x+4y= 7
2x-4y= 13
*Do: Identify opposite terms. Yell out ‘elimination!’ when you got it.
Step 2:
“add” equations,
Eliminating
opposite terms
Say: Now we add the equations, just like we would add numbers. So we only add like terms
together. So and as we will see our y will cancel and we will be left with our x’s.
Step 3:
Solve for the
leftover variable
Say: Next step is to solve for x, since it’s the only variable we have left. Our LEFTOVER
variable. Now what is x?
See: 5x = 20
*Do: Students solve for x by dividing both sides by 5. X=4
Say: Now that we know x can we find y? [YES!] How can we do this? By substituting our x
value which is 4, back into one of the original equations. So let’s use the first equation to
substitute 4 in for x and then solve for y.
See: 3*4 + 4y = 7
12 + 4y = 7
4y= -5
Y= (-5/4)
*Do: Now quietly, use other equation 2x-4y= 13 to see if we get the same value for y. (3mins)
2*4 – 4y =13
8 – 4y = 13
-4y = 5
Y = (5/-4) = (-5/4)
So our solution is what ordered pair (x,y) = (4, -5/4)
Say: Last step is to check our solution to make sure its correct, and we do this by plugging our
solution into our two equations. So let’s check the first equation, 3x + 4y =7. If we get a true
statement (5=5) then it correct.
See: 3*4 + 4* (-5/4) =7
12 + -5 = 7
7= 7
*Do: Check solution for other equation. What true statement do you get? (13=13)
Say:
See:
*Do:
Step 4:
Substitute that
leftover value
into one
equations, solve
for the new
variable
Step 5:Check
solution by
plugging values
into the original
equations
Step 6:
See: 5x + 0 = 20
*Do: Copy it down. When you got, say ‘I got it!’
PRACTICE
*Structured Practice (3-4 additional examples led by teacher with gradually quickening pace, helping students
approach automaticity by manipulating time, materials, and group size)
Time:
3x + 2y =7
Materials:
5x-2y = 9
Group Size:
Time:
X+ 7y = 13
Materials:
x-7y = 5
Group Size:
Time:
What if we have an equation that does not have opposite terms? We create our opposite terms
Materials:
by multiplying whole equations numbers.
Group Size:
So if we have the two equations.
2x+ 3y =1
5x + 7y = 3
Say: So let’s eliminate the x variable so we will be concentrating on that. How can we get 2x
and 5x the same?
We can multiply the top equation by 5 to get 10x
And we can multiply the bottom one by 2 to get 10x.
But 10x and 10x don’t cancel. So we need one of them to be negative,let’s pick 2 to be
negative so now they will cancel. Remember you have to multiply the whole equation by the 5
or 2. NOT just the terms you want to eliminate.
See: (5)*2x + (5)3y = (5)*1
(-2)*5x + (-2)7y = (-2)*3
->
->
10x + 15y = 5
-10x – 14y = -6
Do: “So now we have opposite terms so we can perform the steps from earlier, now solve for x
and y. (2,-1) . Once you think you got the answer yell “I got it!”
Check answers together.
Time:
Materials:
Group Size:
You wont always have to multiply both equations by number especially if for a pair of terms
one of the coefficient is 1 or -1.
So let’s look at this system.
2p + 3q =18
5p – q = 11
So if we look at q terms. We see 3q and –q. So what can we multiply the bottom equations by? (three).
Then we get opposite terms.
2P +3q= 18
-> 2p+3q=18
(3)5p – (3)q = (3)11
-> 15p-3q = 33
Do: Now we can go through steps. Find the point of intersection.
11x + 2y = -8
8x + 3y = 5
In pairs, try to solve this system of equations using elimination.
*Guided Practice (the proving behavior of the objective monitored by the teacher)
Assignment: (from proving behavior)
Criteria for Mastery:
If needed 3 problems
2 out of 3.
-x +2y =12
X + 6y = 20
2x = 3y-12
(1/3)x = 4y + 5
3x-2y = 2
4x – 7y = 33
Independent Practice (Homework)
Explain Homework:
Complete 5 elimination problems in packet.
CLOSURE
Explain Closure:
Think. Pair.Share.
Which method do you prefer to solve Systems of Equations, graphing, substitution, elimination?
Why?
VIP