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Main Idea and New Vocabulary
NGSSS
Example 1: Solve a System by Substitution
Example 2: Real-World Example
Example 3: Real-World Example
Five-Minute Check
• Solve systems of equations by substitution.
• substitution
MA.8.A.1.3 Use tables, graphs, and models to
represent, analyze, and solve real-world
problems related to systems of linear
equations.
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 + 15
Write the equation.
4x =
x + 15
Replace y with 4x.
–x
–x
3x = 15
Subtract x from each side.
Simplify.
Solve a System by Substitution
3
3
x =5
Divide each side by 3.
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)
Solve the system of equations by substitution.
y=x–7
y = 2x
A. (–7, –14)
B. (0, –7)
C. (7, 0)
D. (7, 14)
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.
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.
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
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.
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). 
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.
Solve the system of equations by substitution.
y = 2x + 3
y = 12
A. (4.5, 12)
B. (7.5, 12)
C. (12, 4.5)
D. (12, 27)
Solve the system of equations by substitution.
y=x–6
y=3
A. (–3, 3)
B. (2, 3)
C. (3, 9)
D. (9, 3)
Solve the system of equations by substitution.
y=x–4
y=
x
A. (–6, –10)
C.
(6, 2)
B. (–3, –1)
D.
(12, 8)
Solve the system of equations by substitution.
y = –4x – 8
y = –2x
A. (−8, 16)
B. (−4, −8)
C. (−4, 8)
D. (2, –4)
Together, Wally and Sam have 20 toy trains. Wally
has 8 more trains than Sam. How many trains
does each boy have?
A. Sam has 14 trains and Wally has 6 trains.
B. Sam has 6 trains and Wally has 14 trains.
C. Sam has 8 trains and Wally has 12 trains.
D. Sam has 10 trains and Wally has 28 trains.