Solving by Substitution Lesson

Solve Systems by Substitution

Solve the following system of equations:

y = 5/2x + 20

x = 4

Fill in the Blank

What will y equal if we plug in the value 4 for x?

y = 5/2x + 20

x=4

5/2(4)+20=?

Solve the following system of equations:

y = 5/2x + 20

x = 4

​y=5/2(4)+20

​y=5/2(x)+20

​y=30

​y=10+20

​Therefore, the SOLUTION is the ordered pair (4,30)!

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​When we are given equations that have both the x and y variable in them, we should give values for both the x and y variable!
Ordered pairs! (x,y)

Solve the following system of equations:

y = -7/2x - 13

x = -4

Fill in the Blank

What is the solution to the system:

y = -7/2x - 13

x = -4

Reminder! Your answer should be written as an ordered pair! (x,y)

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Solve the following system of equations:

y = -4

8x + 3y = -12

Fill in the Blank

What is the solution to the system:

y = -4

8x + 3y = -12

Reminder! Your answer should be written as an ordered pair! (x,y)

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Solve the following system of equations:

y = -3x

y = -4x + 1

Solve the following system of equations:

y = -3x

y = -4x + 1

​Replace the 2nd y with what the first y is equal to!

-3x = -4x+1

Now we have an equation to solve!

Fill in the Blank

Solve the equation:

-3x = -4x+1

=

Solve the following system of equations:

y = -3x

y = -4x + 1

​Replace the 2nd y with what the first y is equal to!
-3x = -4x+1
Now we have an equation to solve!

x=1

Plug in the x value to find the y value!

y=-3x --> y=-3(1) --> y=-3

Solve the following system of equations:

y = -3x

y = -4x + 1

​Replace the 2nd y with what the first y is equal to!
-3x = -4x+1
Now we have an equation to solve!

x=1

Plug in the x value to find the y value!

y=-3x --> y=-3(1) --> y=-3


Solution: (1,-3)

Solve the following system of equations:

y = 2x - 2

y = x - 3

Fill in the Blank

Solve the following system of equations:

y = 2x - 2

y = x - 3

Reminder! Your answer should be written as an ordered pair! (x,y)

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Solve the following system of equations:
y = 2x - 2
y = x - 3

Solve the following system of equations:
y = 2x - 2
y = x - 3

2x-2=x-3
-x -x
x-2=-3
+2 +2
x=-1

​y=2x-2
y=2(-1)-2
y=-2-2
y=-4

Solution: (-1,-4)

Solve the following system of equations:

y = 5x - 18

y = -6x + 4

Fill in the Blank

Solve the following system of equations:

y = 5x - 18

y = -6x + 4

Reminder! Your answer should be written as an ordered pair! (x,y)

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Solve the following system of equations:

y = 2x

-5x + 3y = -1

​We know y = 2x
When looking at the other equation, I can replace y with 2x.
-5x+3(2x)=-1

​​We know y = 2x.
When looking at the other equation, I can replace y with 2x.
-5x+3(2x)=-1
Now we can solve this equation
-5x+6x=-1
1x=-1
x=-1

Now let's find y

​​​We know y = 2x.
When looking at the other equation, I can replace y with 2x.
-5x+3(2x)=-1
Now we can solve this equation -5x+6x=-1
1x=-1
x=-1
Now let's find y!

​y=2x
We just found out x=-1
Let's plug in x!


y=2x
y=2(-1)
y=-2


Solution: (-1,-2)

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Solve the following system of equations:

x = 2y

4x + 2y = 20

Fill in the Blank

Solve the following system of equations:

x = 2y

4x + 2y = 20

Reminder! Your answer should be written as an ordered pair! (x,y)

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Solve the following system of equations:

y = -2x + 3

4x + 3y = 5

​This one is a little spicier!
y=-2x+3
4x+3y=5

y=-2x+3
4x+3y=5
4x+3(y)=5
4x+3(-2x+3)=5
Now we can solve this equation!

​4x+3(-2x+3)=5
4x+-6x+9=5
-2x+9=5
-9 -9
-2x=-4
-2 -2
x=2

​Now let's find y!
y=-2x+3
We found out that x=2
y=-2(2)+3
y=-4+3
y=-1

​Solution: (2,-1)

Solve the following system of equations:

y = 2x + 6

-4x + 5y = 18

Fill in the Blank

Solve the following system of equations:

y = 2x + 6

-4x + 5y = 18

Reminder! Your answer should be written as an ordered pair! (x,y)

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Solve the following system of equations:

-6x + 3y = -12

x = 4y + 9

Fill in the Blank

Solve the following system of equations:

-6x + 3y = -12

x = 4y + 9

Reminder! Your answer should be written as an ordered pair! (x,y)

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Yay! Great job. I'm so proud of you for completing this :)

Now go dilly dally.