1. Solving Systems by Elimination (Part 1 – Addition/Subtraction) Students will be able to solve systems exactly by using addition or subtraction to eliminate one variable.

2. A method that works best when both equations are in standard form
A method that works best when both equations are in standard form. If a variable has either the same or opposite coefficients you can eliminate it by adding or subtracting the equations together, leaving only one remaining variable to solve for. {
Elimination Method
3x – 4y = x + 4y = 8 {
7x - 2y = x - 2y = 8

3.  Ex1: Solve by elimination. Explain -5x – 3y = 23 + 5x + 2y = -27 -1y
 Identify the variable you want to cancel (find opposite coefficients) +
5x + 2y = -27
-1y
= -4 -1 -1
 Add equations to cancel x and solve for y.
y = 4
5x + 2y = -27
 Substitute y = 4 into either starting equation. 5x
+ 2(4)
= -27
Solution (-7, 4) 5x
+ 8
= -27
Once students find y = 4 their can substitute it into either starting equation. As they do the guided practice problems their steps may not match with the one demonstrated on the powerpoint but as long as their answer is correct they are doing great.
– 8 -8
 Solve for x. 5x
= -35
 Write solution. 5 5
x = -7

4. Guided Practice Solve by elimination. x + 4y = 4 + -5x – 4y = 12 -4x
= 16 -4 -4
x = -4
x + 4y = 4 -4
+ 4y
= 4
Solution (-4, 2) +4 +4 4y
= 8 4 4
y = 2

5. Guided Practice Solve by elimination. 2x + 5y = -2 + -2x + 5y = -18
= -20 10 10
y = -2
2x + 5y = -2 2x
+ 5(-2)
= -2
Solution (4, -2) 2x
– 10
= -2
+10
+10 2x
= 8 2 2
x = 4

6. Guided Practice Solve by elimination. -5x – 4y = -11 + x + 4y = -1 -4x
= -12 -4 -4
x = 3
-5x – 4y = -11
-5(3)
– 4y
= -11
Solution (3, -1)
-15
– 4y
= -11
+15
+15
-4y
= 4 -4 -4
y = -1

7. Guided Practice Solve by elimination. -6x + 4y = -5 + 6x – 4y = 5 = 0
= 0
True!
Infinite Solutions

8. Guided Practice Solve by elimination. -x – 3y = 6 + x + 4y = -9 1y
= -3 1 1
y = -3
-1x – 3y = 6
-1x
– 3(-3)
= 6
Solution (3, -3)
-1x
+ 9
= 6 -9 -9
-1x
= -3 -1 -1
x = 3

9. Elimination Flow Chart
Does a variable have the same or opposite coefficients?
Elimination Flow Chart
Yes No
Does that variable have an opposite coefficient?
Yes No No
Yes
SUBTRACT SYSTEMS (cancelling out the variable)
ADD SYSTEMS (cancelling out the variable)

10.  Ex2: Solve by Elimination Explain x – 2y = 8 - 3x – 2y = 4 -2x = 4
 Identify the variable you want to cancel. (Same coefficient/Same sign) x
– 2y
= 8
x – 2y = 8
3x – 2y = 4 -
3x – 2y = 4
-2x
= 4 -2 -2
 Subtract equations to cancel y and solve for x.
x = -2
3x – 2y = 4
3(-2)
– 2y
= 4
 Substitute x = -2 into either starting equation. -6
– 2y
= 4
Solution (-2, -5)
Remind students they can multiply either equation by -1 and still get the correct answer. I prefer to have students multiply by -1 rather than subtracting the linear equations. This gives then practice with multiplying equations and keeps them from having trouble when they have to subtract a negative. +6 +6
 Solve for y.
-2y
= 10 -2 -2
 Write solution.
y = -5

11. Guided Practice Solve by elimination. -3x + 2y = -16 -3x + 4y = -8 -3x
= -8 -2 -2
-3x + 2y = -16
y = 4
-3x
+ 2(4)
= -16
-3x
+ 8
= -16
Solution (8, 4) -8 -8
-3x
= -24 -3 -3
x = 8

12. Guided Practice Solve by elimination. 2x + 4y = -8 x + 4y = -18 2x
= 10
2x + 4y = -8
x = 10
2(10)
+ 4y
= -8 20
+ 4y
= -8
Solution (10, -7)
-20
-20 4y
= -28 4 4
y = -7

13. Guided Practice Solve by elimination. -7x + 3y = 5 -7x + 3y = -10 -7x
= 5 -
-7x + 3y = -10
= -15
False!
No Solutions

14. Guided Practice Solve by elimination. 5x + 6y = -8 5x – 3y = 19 5x
= -27 9 9
5x + 6y = -8
y = -3 5x
+ 6(-3)
= -8 5x
– 18
= -8
Solution (2, -3)
+18
+18 5x
= 10 5 5
x = 2

15. Guided Practice Solve by elimination. x – y = -16 -5x – y = 32 x - 1y
= -48 6 6
x – y = -16
x = -8 -8
– y
= -16 +8 +8
Solution (-8, 8)
-1y
= -8 -1 -1
y = 8

16. Tips for the lesson
Have students record vocabulary and examples in their notes. If you want to grade guided practice as part of their classwork grade have them staple it and hand it in with their classwork or homework. Use guided practice time to call on students and assess the class.
Students should not need calculators. I made numbers reasonable enough to do in their head on the guided practice as well as on the homeworks, classworks, quizzes, and test.
Because these problems are longer and require a lot of computation don’t be surprised if you catch students making mistakes with their negatives. It’s be useful to have students to work in pairs so they can compare answer and fix each other’s mistakes.
I am so excited about the Elimination Flow Chart I added to this lesson! I included both a blank flow chart and one filled out so you can print out either one for your students to use. I’d suggest using the blank outline because drawing the whole thing in their notes might be a bit tricky. If you don’t like the wording please feel free to change it. The first day of elimination is always pretty easy for students but when you enter the second day of elimination the flow chart can be very helpful for students as they determine not only which variable to eliminate but how to go about doing it.

17. Elimination Flow Chart
Does a variable have the same coefficients?
Yes No
Does that variable also have opposite signs?
Is the coefficient of one variable a factor of the other?
Yes No No
Yes
Multiply one equation (the one with the smaller coefficient) by a factor of the other.
Multiply BOTH equations with each others’ coefficients.
Multiply one equation by a negative
ADD SYSTEMS (cancelling out the variable)

18. Elimination Flow Chart
Does a variable have the same or opposite coefficients?
Yes No
Does that variable have an opposite coefficient?
Is the coefficient of one variable a factor of the other?
Yes No No
Yes
Multiply one equation (the one with the smaller coefficient) by a factor of the other.
Multiply BOTH equations with each others’ coefficients.
ADD SYSTEMS (cancelling out the variable)
SUBTRACT SYSTEMS (cancelling out the variable)