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Solving Systems of Equations
Today’s Lesson
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Warm-Up Activity
We will warm up today by working with equations.
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5x + 7 = 32– 7 – 7
5x = 25÷ 5 ÷ 5
x = 5
Solve the equation.
Check your answer using substitution. If the left and right side match, you have the correct answer.
5(5) + 7 = 3225 + 7 = 32
32 = 32
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Solve and check your work using substitution.
3x – 7 = 14
x = 7
3(7) – 7 = 1421 – 7 = 14
14 = 14
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Solve and check your work using substitution.
x + 3 = –15
x = 27
(27) + 3 = –15– 18 + 3 = –15
–15 = –15
3
2
3
2
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Solve and check your work using substitution.
x – 8= 36
x = 176
(176) – 8 = 3644 – 8 = 36
36 = 36
4
1
4
1
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Today, you will solve systems of two linear equations with two variables using the substitution method.
Whole-Class Skills Lesson
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Kimo and Sadi had a total of 8 wooden cars. Each of Kimo’s cars cost $2. Each of Sadi’s cars cost $3. Kimo and Sadi spent a total of $19. How many cars does Kimo have? How many cars does Sadi have?
How many equations can be written from the information in the problem?
x = the number of Kimo’s cars
y = the number of Sadi’s cars
two equations
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Write an equation for the total number of cars.
x + y = 8
Kimo and Sadi had a total of 8 wooden cars. Each of Kimo’s cars cost $2. Each of Sadi’s cars cost $3. Kimo and Sadi spent a total of $19. How many cars does Kimo have? How many cars does Sadi have?
x = the number of Kimo’s carsy = the number of Sadi’s cars
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Write an equation for the amount of money spent for all the cars.
2x + 3y = 19
Kimo and Sadi had a total of 8 wooden cars. Each of Kimo’s cars cost $2. Each of Sadi’s cars cost $3. Kimo and Sadi spent a total of $19. How many cars does Kimo have? How many cars does Sadi have?
x = the number of Kimo’s cars
y = the number of Sadi’s cars
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x + y = 8
Sub in for x to find y.
x y
2
3
4
5
6
5
43
x
y
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2x + 3y = 19
Sub in for x to find y.
x y
3
4
5
6
4.33
3.66
32.33
x
y
x + y = 8
1
1
2
2
2x + 3y = 19
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Where do the lines intersect?
x
y
x + y = 8
1
1
2
2
2x + 3y = 19
(5, 3)
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What does the point, (5, 3) represent?
x
y
x + y = 8
1
1
2
2
2x + 3y = 19 (5, 3)x = 5 y = 3Kimo has 5 cars.Sadi has 3 cars.
x = the number of Kimo’s cars
y = the number of Sadi’s cars
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x + y = 8
Solve the system of equation without graphing. Remember you can use substitution.
2x + 3y = 19
We can rewrite the first equation so x is by itself on the left side of the equation.
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x + y – y = – y + 8
Use inverse operations to get the x by itself.
Subtract y from both sides of the first equation.
x = – y + 8
x + y = 8
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Substitute the new equation in for x.
x = – y + 8
2x + 3y = 19
2(– y + 8) + 3y = 19
– 2y + 16 + 3y = 19
y = 3
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x = – (3) + 8
y = 3
x = 5
(5 , 3)
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Write an equation for the total number of cards.
x + y = 64
Chad and Craig have 64 baseball card all together. Chad paid 4 dollars for each of his cards, and Craig paid 2 dollars for each of his card. How many baseball cards do each of the boys have?
x = the number of Chad’s cardsy = the number of Craig’s cards
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Write an equation for the amount of money spent for all the cards.
4x + 2y = 184
Chad and Craig have 64 baseball card all together. Chad paid 4 dollars for each of his cards, and Craig paid 2 dollars for each of his card. Together they have spent a total of $184. How many baseball cards do each of the boys have?
x = the number of Chad’s cards
y = the number of Craig’s cards
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x + y = 64
4(– y + 64) + 2y = 184
Solve the system by using substitution.
x = – y + 64
4x + 2y = 184
– 2y = – 72
y = 36
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x + y = 64
If y = 36 then sub in to find x.
x + 36 = 64
x = 28
(28, 36)
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Chad and Craig have 64 baseball card all together. Chad paid 4 dollars for each of his cards, and Craig paid 2 dollars for each of his card. How many baseball cards do each of the boys have?
x = the number of Chad’s cardsy = the number of Craig’s cards
(28, 36)
Chad has 28 baseball cards and Craig has 36 baseball cards.