1. Solving Linear Systems with Substitution
Section 3.2a
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3.2a - Solving Systems through Substitution

2. 3.2a - Solving Systems through Substitution
Steps in Substitution
SOLVE for one equation into one variable
REPLACE one equation into other equation
SUBSTITUTE the value into either equation
CHECK the solution
HINT: BEST TIME TO USE SUBSTITUTION IS WHEN AN EQUATION HAS AN ISOLATED VARIABLE
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3.2a - Solving Systems through Substitution

3. 3.2a - Solving Systems through Substitution
Example 1
Solve using Substitution
1. SOLVE for one equation into one variable
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3.2a - Solving Systems through Substitution

4. 3.2a - Solving Systems through Substitution
Example 1
Solve using Substitution
2. REPLACE one equation into other equation
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3.2a - Solving Systems through Substitution

5. 3.2a - Solving Systems through Substitution
Example 1
Solve using Substitution
2. REPLACE one equation into other equation
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3.2a - Solving Systems through Substitution

6. 3.2a - Solving Systems through Substitution
Example 1
Solve using Substitution
3. SUBSTITUTE the value into either equation
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3.2a - Solving Systems through Substitution

7. 3.2a - Solving Systems through Substitution
Example 1
Solve using Substitution
3. SUBSTITUTE the value into either equation
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3.2a - Solving Systems through Substitution

8. 3.2a - Solving Systems through Substitution
Example 1
Solve using Substitution
4. CHECK the solution
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3.2a - Solving Systems through Substitution

9. 3.2a - Solving Systems through Substitution
Example 2
Solve using Substitution
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3.2a - Solving Systems through Substitution

10. 3.2a - Solving Systems through Substitution
Your Turn
Solve using Substitution
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3.2a - Solving Systems through Substitution

11. 3.2a - Solving Systems through Substitution
Example 3
Solve using Substitution
1. SOLVE for one equation into one variable
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3.2a - Solving Systems through Substitution

12. 3.2a - Solving Systems through Substitution
Example 3
Solve using Substitution
2. REPLACE one equation into other equation
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3.2a - Solving Systems through Substitution

13. 3.2a - Solving Systems through Substitution
Example 3
Solve using Substitution
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3.2a - Solving Systems through Substitution

14. 3.2a - Solving Systems through Substitution
Example 3
Solve using Substitution
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3.2a - Solving Systems through Substitution

15. 3.2a - Solving Systems through Substitution
Example 4
Solve using Substitution
1. SOLVE for one equation into one variable
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3.2a - Solving Systems through Substitution

16. 3.2a - Solving Systems through Substitution
Example 4
Solve using Substitution
2. REPLACE one equation into other equation
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3.2a - Solving Systems through Substitution

17. 3.2a - Solving Systems through Substitution
Example 4
Solve using Substitution
3. SUBSTITUTE the value into either equation
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3.2a - Solving Systems through Substitution

18. 3.2a - Solving Systems through Substitution
Example 4
Solve using Substitution
3. SUBSTITUTE the value into either equation
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3.2a - Solving Systems through Substitution

19. 3.2a - Solving Systems through Substitution
Example 4
Solve using Substitution
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3.2a - Solving Systems through Substitution

20. 3.2a - Solving Systems through Substitution
Your Turn
Solve using Substitution
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3.2a - Solving Systems through Substitution

21. 3.2a - Solving Systems through Substitution
Application Steps
Read the question, TWICE
Understand and TRANSLATE the QUESTION
Identify all variables by appropriately LABELING (this is required)
SOLVE using Substitution or Elimination and label accordingly
CHECK answer
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3.2a - Solving Systems through Substitution

22. How much of each type of coffee is in 50 lb of the blend?
Example 5
A coffee blend contains Sumatra beans which cost $5/lb., and Kona beans, which cost $13/lb. If the blend costs $10/lb., how much of each type of coffee is in 50 lbs. of the blend?
How much of each type of coffee is in 50 lb of the blend?
Let x represent the amount of the Sumatra beans in the blend.
Let y represent the amount of the Kona beans in the blend.
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3.2a - Solving Systems through Substitution

23. Amount of Sumatra beans
Example 5
A coffee blend contains Sumatra beans which cost $5/lb., and Kona beans, which cost $13/lb. If the blend costs $10/lb., how much of each type of coffee is in 50 lbs. of the blend?
Write one equation based on the amount of each bean:
Amount of Sumatra beans
plus
amount of Kona beans
equals x y
50. 50 + =
Write another equation based on cost of the beans:
Cost of Sumatra beans
plus
cost of Kona beans
equals 5x
13y
cost of beans.
10(50) + =
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3.2a - Solving Systems through Substitution

24. 3.2a - Solving Systems through Substitution
Example 5
A coffee blend contains Sumatra beans which cost $5/lb., and Kona beans, which cost $13/lb. If the blend costs $10/lb., how much of each type of coffee is in 50 lbs. of the blend?
Solve the system.
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3.2a - Solving Systems through Substitution

25. 3.2a - Solving Systems through Substitution
Example 5
A coffee blend contains Sumatra beans which cost $5/lb., and Kona beans, which cost $13/lb. If the blend costs $10/lb., how much of each type of coffee is in 50 lbs. of the blend?
Solve the system.
The mixture will contain lb of the Sumatra beans and lb of the Kona beans.
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3.2a - Solving Systems through Substitution

26. 3.2a - Solving Systems through Substitution
Assignment
WKST Substitution
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3.2a - Solving Systems through Substitution