I can solve systems of equations
by substitution
Warm Up
1.
𝟒
Graph 𝒚 = − 𝒙 +
𝟓
𝟔
𝟖
Solve:
=
𝟑𝒙−𝟐
𝟒𝒙−𝟏
𝟗
2.
3. Write a system of equations:
Sara has 16 baseball cards and buys 7 more
each week. Ted has 2 baseball cards and
collects 9 more each week. Write a systems
of equations and solve to find out when
they will have the same number of cards.
I can solve systems of equations
by substitution
Warm Up
1. Graph 𝒚 =
𝟒
− 𝒙
𝟓
+𝟗
I can solve systems of equations
by substitution
Warm Up
Solve:
𝟔
𝟑𝒙−𝟐
=
𝟖
𝟒𝒙−𝟏
I can solve systems of equations
by substitution
Warm Up
Write a system of equations:
Sara has 16 baseball cards and buys 7 more
each week. Ted has 2 baseball cards and
collects 9 more each week. Write a systems
of equations and solve to find out when
they will have the same number of cards.
Homework Questions
Diamond Problems
xy
x
y
x+y
4
-8
Diamond Problems
-42
xy
x
y
x+y
3
-14
-11
Diamond Problems
xy
x
y
x+y
-64
16
12
-4
Solve the following system using
any method
3𝑥 + 2𝑦 = 12
𝑦 =𝑥−3
Solve by Graphing
3𝑥 + 2𝑦 = 12
2𝑦 = −3𝑥 + 12
3
𝑦 =− 𝑥+6
2
𝑦 =𝑥−3
The solution isn’t at a clear point!
What else could we try?
3𝑥 + 2𝑦 = 12
𝑦 =𝑥−3
Try it!
• Try problems 1 and 2 on your practice sheet
using the method we just discovered. See if
you can solve the systems
Solving Systems with Substitution
Steps
1. Determine variable to
substitution
2. Make substitution
3. Solve
Example:
3𝑦 − 2𝑥 = 11
𝑦 = −2𝑥 + 9
**Substitute in for y
3 −2𝑥 + 9 − 2𝑥 = 11
−6𝑥 + 27 − 2𝑥 = 11
−8𝑥 + 27 = 11
−27 − 27
−8𝑥 = −16
𝑥=2
Solving Systems with Substitution
Steps
4. Plug back into an
original equation
5. Solve for missing
variable
6. Write answer as a
point
Example:
3𝑦 − 2𝑥 = 11
𝑦 = −2𝑥 + 9
𝑥=2
𝑦 = −2(2) + 9
𝑦 = −4 + 9
𝑦=5
(2, 5)
Practice
20 minutes
Check your
answers on
the back table
Writing and Solving Systems
April sold 75 tickets to a school play and
collected a total of $495. If the adult tickets
cost $8 each and child tickets cost $5 each,
how many adult tickets and how many child
tickets did she sell?
April sold 75 tickets to a school play and collected a
total of $495. If the adult tickets cost $8 each and
child tickets cost $5 each, how many adult tickets
and how many child tickets did she sell?
Define variables:
a = the number of adult tickets.
c = the number of child tickets.
System of equations:
a + c = 75
8a + 5c = 495
State your solution(s):
There were 40 adult tickets and 35 child tickets
sold.
40 + 35 = 75
8(40) + 5(35) = 495
320 + 175 = 495
Solve
a + c = 75
8a + 5c = 495
a = 75 – c
8(75 – c) + 5c = 495
600 – 8c + 5c = 495
600 - 3c = 495
105 = 3c
35 = c
a + c = 75
a + 35 = 75
a = 40
Writing and Solving Systems
At a baseball game, Jose
bought four hot dogs
and one soda for $12.
At the same time,
Allison bought two hot
dogs and four sodas for
$13. Find the cost of
one hot dog and one
soda.
At a baseball game, Jose bought four hot dogs and
one soda for $12. At the same time, Allison bought
two hot dogs and four sodas for $13. Find the cost
of one hot dog and one soda.
Define variables:
h = the price of hot dog.
s = the price of a soda.
System of equations:
4h + s = 12
2h + 4s = 13
State your solution(s):
A hot dog costs $2.50 and a soda costs
$2.00.
4(2.5) + 2 = 12
2(2.5) + 4(2) = 13
5 + 8 = 13
Solve
4h + s = 12
2h + 4s = 13
s = 12 – 4h
2h + 4(12 – 4h) = 13
2h + 48 – 16h = 13
48 – 14h = 13
35 = 14h
2.5 = h
4h + s = 12
4(2.5) + s = 12
10 + s = 12
s=2
Homework
Textbook