1. Solving Systems of Equations By Substitution
A-REI.3; A-REI.5; A-REI.6; A-REI.7

2. Table of Contents
46: Warm-Up
47: How Do I Solve a System of Equations by Substitution?

3. Warm-Up
Solve the system of equations and state the solution as an ordered pair. Hint: Solve the equations for y 1. x + 2y = 6 g(x) = ½x h(x) = x + 3y = -6

4. Warm-Up 1. x + 2y = 6 g(x) = ½x - 1 x + 2y = 6 - x - x _____________
__ 2
__ 2
__ 2
y = - ½x + 3
Solution:
(4, 1)

5. Warm-Up 2. h(x) = 2 -2x + 3y = -6 +2x +2x _____________ __ 3
__ 3
3y = 2x – 6
__ 3
__ 3
y = 2x –
Solution:
(6, 2)

6. Learning Intention/Success Criteria
LI: We are learning how to solve a system of equations by substitution SC: I know how to -determine if a system of equations has many, none, or no solutions -solve systems of two linear equations algebraically using substitution method -solve equations for a variable

7. EQ: How Do I Solve a System of Equations by Substituting?
11/14/2018

8. Fold the paper in half, hot dog style
Cut along the fold, making two strips of paper

9. Take one piece and lay it flat

10. Take the other piece of paper and place it on top of the first
Take the other piece of paper and place it on top of the first. Make sure to leave a space at the bottom

11. Fold the second piece down and leave a space to writing

12. Fold the first piece down and leave a space to writing
Staple
Staple

13. Solving Systems with Substitution
No Solutions
Many Solutions
One Solution

14. Open the foldable so that you can write on the one solution page

15. { 3x + 2y = 10 x – 2y = 6 1. Solve an equation for a variable
___________
x = 2y + 6
One Solution

16. x = 2y + 6
2. Substitute eq
3. Substitute value
x = 2y + 6 3x + 2y = 10
3x + 2y = 10 y = -1
3(2y + 6) + 2y = 10
3x + 2(-1) = 10
+ 2y = 10 6y
+ 18
3x + -2 = 10 +2 +2
____________
8y + 18 = 10
3x = 12
__ 3
__ 3
x = 4
____________
-18
-18
8y = -8
__ 8
__ 8
4. Solution:
(4, -1)
y = -1
One Solution

17. { Guided Practice 1 Find the solution to the system by substitution:
y = 2x – 4 x + 3y = 9 {
x + 3y = 9 -2x + y = -4
x + 3(2x – 4) = 9
x = 3 -2x + y = -4
x + 6x
- 12
= 9
-2x + y = -4
+2x
+2x
7x – 12 = 9
__________
-2(3) + y = -4
+12
y = 2x - 4
___________
+12
-6 + y = -4
7x = 21
__ 7
__ 7 +6 +6
___________
(3, 2) One Solution
y = 2
x = 3

18. Solving Systems with Substitution
No Solutions
Many Solutions
One Solution

19. Open the foldable so that you can write on the many solution page
Many Solutions
One Solution

20. { 4x - 2y = -10 -2x + y = 5 1. Solve an equation for a variable
____________
y = 2x + 5
Many Solutions
One Solution

21. y = 2x + 5 2. Substitute eq 3. Answer 4x – 2y = -10 y = 2x + 5
Many Solutions
When graphed, the lines are the same.
4x -2(2x + 5) = -10 4x
- 4x
- 10
= -10
0x – 10 = -10
– 10 = -10
Many Solutions
One Solution

22. { Guided Practice 2 Find the solution to the system by substitution:
9x – 3y = -15 y = 3x + 5 {
9x – 3y = -15 y = 3x + 5
9x – 3(3x + 5) = -15 9x
-9x
- 15
= -15
0x – 15 = -15
- 15 = -15
Many Solutions

23. Solving Systems with Substitution
No Solutions
Many Solutions
One Solution

24. Open the foldable so that you can write on the many solution page
No Solutions
Many Solutions
One Solution

25. { x – 2y = 3 2x -4y = 1 1. Solve an equation for a variable x – 2y = 3
____________
+2y
x = 2y + 3
No Solution
Many Solutions
One Solution

26. x = 2y + 3 x = 2y + 3 2x -4y = 1 2. Substitute eq 3. Answer
No Solution
When graphed, the lines will never pass
2(2y + 3) – 4y = 1 4y
+ 6
- 4y = 1
The lines are parallel
0y + 6 = 1
6 = 1
No Solution
Many Solutions
One Solution

27. { Guided Practice 3 Find the solution to the system by substitution:
y = 2x -2x + y = 4 {
-2x + y = 0 -2x + y = 4
-2x + 1(2x) = 4
-2x + 2x = 4
-2x + y = 0
+2x
+2x
0 = 4
______________
y = 2x
No Solution