2. Main Idea and New Vocabulary Example 1: Solve a System by Substitution
Example 2: Real-World Example
Example 3: Real-World Example
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3. Solve systems of equations by substitution.
Main Idea/Vocabulary

4. Solve a System by Substitution
Solve the system of equations by substitution.
y = x + 15
y = 4x
Since y is equal to 4x, you can replace y with 4x in the first equation.
y = x Write the equation.
4x = x Replace y with 4x.
– x – x Subtract x from each side.
3x = 15 Simplify.
Example 1

5. Solve a System by Substitution3
Divide each side by 3.
x = 5 Simplify.
Since x = 5 and y = 4x, then y = 20 when x = 5. The solution of this system of equations is (5, 20). Check the solution by graphing.
Answer: (5, 20)
Example 1

6. Solve the system of equations by substitution. y = x – 7 y = 2x
C. (7, 0)
D. (7, 14)
Example 1 CYP

7. Draw a bar diagram. Then write the system.
SALES A store sold 84 black and gray T-shirts one weekend. They sold 5 times as many black T-shirts as gray T-shirts. Write a system of equations to represent this situation.
Draw a bar diagram. Then write the system.
Example 2

8. x + y = 84 The total number of black and gray T-shirts is 84.
Let x represent the number of black T-shirts and y represent the number of gray T-shirts.
x + y = 84 The total number of black and gray T-shirts is 84.
x = 5y There were 5 times as many black T-shirts as gray T-shirts.
Answer: The system of equations is x + y = 84 and x = 5y.
Example 2

9. FAIR Devin and Emily spent a total of $24 at the fair
FAIR Devin and Emily spent a total of $24 at the fair. Devin spent three times as much as Emily spent. Let x represent the amount Emily spent and let y represent the amount Devin spent. Write a system of equations to represent this situation.
A. x − y = 24 x = 3y
B. 3x + y = 24 y = 3x
C. x + y = 24 y = 3x
D. x + y = 24 x = 3y
Example 2 CYP

10. x + y = 84 Write the equation. 5y + y = 84 Replace x with 5y.
SALES A store sold 84 black and gray T-shirts one weekend. They sold 5 times as many black T-shirts as gray T-shirts. Solve the system by substitution. Interpret the solution.
The system of equations is x + y = 84 and x = 5y. Since x is equal to 5y, you can replace x with 5y.
x + y = 84 Write the equation.
5y + y = 84 Replace x with 5y.
6y = 84 Simplify.
Divide each side by 6.
y = 14 Simplify.
Example 3

11. Since y = 14 and x = 5y, then x = 70 when y = 14.
Answer: The solution is (70, 14). This means that the store sold 70 black and 14 gray T-shirts.
Check Check the solution by graphing.
The graphs of the functions intersect at the point (70, 14). 
Example 3

12. A. (18, 6); Emily spent $18 and Devin spent $6.
FAIR Devin and Emily spent a total of $24 at the fair. Devin spent three times as much as Emily spent. Let x represent the amount Emily spent and let y represent the amount Devin spent. Solve the system by substitution. Interpret the solution.
A. (18, 6); Emily spent $18 and Devin spent $6.
B. (6, 18); Emily spent $6 and Devin spent $18.
C. (15, 5); Emily spent $15 and Devin spent $5.
D. (5, 15); Emily spent $5 and Devin spent $15.
Example 3 CYP