1. All equations must be solved by the same values of x and y
1 System Word Problems, Elimination, Substitution, & Graphs
Systems of Equations –
More than one equation
All equations must be solved by the same values of x and y

2. ----- Meeting Notes (5/2/17 09:40) -----
three methods
how to find the x and y's that work in all the equations
will do one problem three ways to find x and y

3. 1 System Word Problems, Elimination, Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?

5. Write equations to represent the information given.
1 System Word Problems, Elimination, Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Substitution
Write equations to represent the information given.

6. Write equations to represent the information given.
1 System Word Problems, Elimination, Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Substitution
Write equations to represent the information given.
Tom = 3(Todd)

7. Write equations to represent the information given.
1 System Word Problems, Elimination, Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Substitution
Write equations to represent the information given.
Tom = 3 (Todd)
Tom + 5 = 2(Todd + 5) + 3

8. Replace Tom with 3(Todd) in second equation.
1 System Word Problems, Elimination, Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Substitution
Replace Tom with 3(Todd) in second equation.
Tom = 3 (Todd)
Tom + 5 = 2(Todd + 5) + 3
3 (Todd) + 5 = 2(Todd + 5) + 3

9. 1 System Word Problems, Elimination, Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Substitution
Solve for Todd,
3 (Todd) + 5 = 2(Todd + 5) + 3

10. 3 (Todd) + 5 = 2(Todd + 5) + 3 3(Todd) + 5 = 2(Todd) + 10 + 13
1 System Word Problems, Elimination, Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Substitution
Solve for Todd, then Tom
3 (Todd) + 5 = 2(Todd + 5) + 3
3(Todd) + 5 = 2(Todd)
Todd = 8 years old

11. 1 System Word Problems, Elimination, Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Substitution
Solve for Todd, then Tom
Todd = 8 years old
Tom = 3 (Todd)
Tom = 3(8) = 24 years old

13. Put Tom and Todd on the left side and the constants on the right.
1 System Word Problems, Elimination Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Elimination
Put Tom and Todd on the left side and the constants on the right.
Tom = 3(Todd)
Tom – 3(Todd) = 0

14. Tom + 5 = 2(Todd + 5) + 3 Tom + 5 = 2(Todd) + 10 + 3
1 System Word Problems, Elimination Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Elimination
Put Tom and Todd on the left side and the constants on the right.
Tom + 5 = 2(Todd + 5) + 3
Tom + 5 = 2(Todd)
Tom - 2(Todd) = 8

15. Add or subtract the equations to eliminate Tom or Todd.
1 System Word Problems, Elimination Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Elimination
Add or subtract the equations to eliminate Tom or Todd.
Tom - 2(Todd) = 8
Tom – 3(Todd) = 0

16. Add or subtract the equations to eliminate Tom or Todd.
1 System Word Problems, Elimination Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Elimination
Add or subtract the equations to eliminate Tom or Todd.
Tom + 2(Todd) = 8
- Tom – -3(Todd) = 0
Todd = 8

17. 1 System Word Problems, Elimination Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Elimination
And solve for Tom
Todd = 8 years old
Tom = 3 (Todd)
Tom = 3(8) = 24 years old

19. Replace Tom and Todd with x and y. Let Todd = x Let Tom = y
1 System Word Problems, Elimination Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Graphing
Replace Tom and Todd with x and y.
Let Todd = x
Let Tom = y

20. Replace Tom and Todd with x and y. Let Todd = x Let Tom = y
1 System Word Problems, Elimination Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Graphing
Replace Tom and Todd with x and y.
Let Todd = x
Let Tom = y
Tom = 3 (Todd)
y = 3 x

21. Tom + 5 = 2(Todd + 5) + 3 y + 5 = 2(x + 5) + 3
1 System Word Problems, Elimination Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Graphing
Replace Tom and Todd with x and y.
Let Todd = x
Let Tom = y
Tom + 5 = 2(Todd + 5) + 3
y + 5 = 2(x + 5) + 3

22. Write in slope-intercept form and graph y + 5 = 2 (x+5) + 3
1 System Word Problems, Elimination Substitution, & Graphs
Tom is 3 times as old as Todd. In 5 years Tom’s age will be 3 years more than 2 times as old as Todd. How old is Todd?
Graphing
Write in slope-intercept form and graph
y + 5 = 2 (x+5) + 3
y = 2x – 5
y = 2x + 8

23. y (x,y) = (8,24) x Graphing y = 3 x y = 2x + 8
1 System Word Problems, Elimination Substitution, & Graphs
Graphing
y = 3 x
y = 2x + 8
(x,y) =
(8,24)
Let Todd = x 8 years old
Let Tom = y
24 years old x

24. 1 System Word Problems, Elimination Substitution, & Graphs

25. Later in the week = 4th method : matrices