Splash Screen. Then/Now You solved systems of linear equations by using tables and graphs. Solve...
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Transcript of Splash Screen. Then/Now You solved systems of linear equations by using tables and graphs. Solve...
![Page 1: Splash Screen. Then/Now You solved systems of linear equations by using tables and graphs. Solve systems of linear equations by using substitution. Solve.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f115503460f94c235dd/html5/thumbnails/1.jpg)
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You solved systems of linear equations by using tables and graphs.
• Solve systems of linear equations by using substitution.
• Solve systems of linear equations by using elimination.
![Page 3: Splash Screen. Then/Now You solved systems of linear equations by using tables and graphs. Solve systems of linear equations by using substitution. Solve.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f115503460f94c235dd/html5/thumbnails/3.jpg)
• substitution method
• elimination method
![Page 4: Splash Screen. Then/Now You solved systems of linear equations by using tables and graphs. Solve systems of linear equations by using substitution. Solve.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f115503460f94c235dd/html5/thumbnails/4.jpg)
Use the Substitution Method
FURNITURE Lancaster Woodworkers Furniture Store builds two types of wooden outdoor chairs. A rocking chair sells for $265 and an Adirondack chair with footstool sells for $320. The books show that last month, the business earned $13,930 for the 48 outdoor chairs sold. How many of each chair were sold?
Understand
You are asked to find the number of each type of chair sold.
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Use the Substitution Method
Define variables and write the system of equations. Let x represent the number of rocking chairs sold and y represent the number of Adirondack chairs sold.
x + y = 48 The total number of chairs sold was 48.
265x + 320y = 13,930 The total amount earned was $13,930.
Plan
![Page 6: Splash Screen. Then/Now You solved systems of linear equations by using tables and graphs. Solve systems of linear equations by using substitution. Solve.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f115503460f94c235dd/html5/thumbnails/6.jpg)
Use the Substitution Method
Solve one of the equations for one of the variables in terms of the other. Since the coefficient of x is 1, solve the first equation for x in terms of y.
x + y = 48 First equation
x = 48 – y Subtract y from each side.
![Page 7: Splash Screen. Then/Now You solved systems of linear equations by using tables and graphs. Solve systems of linear equations by using substitution. Solve.](https://reader035.fdocuments.us/reader035/viewer/2022062423/56649f115503460f94c235dd/html5/thumbnails/7.jpg)
Use the Substitution Method
Solve Substitute 48 – y for x in the second equation.
265x + 320y = 13,930 Second equation
265(48 – y) + 320y = 13,930 Substitute 48 – y for x.
12,720 – 265y + 320y = 13,930 Distributive Property
55y = 1210 Simplify.
y = 22 Divide each side by 55.
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Use the Substitution Method
Now find the value of x. Substitute the value for y into either equation.
x + y = 48 First equation
x + 22 = 48 Replace y with 22.
x = 26 Subtract 22 from each side.
Answer: They sold 26 rocking chairs and 22 Adirondack chairs.
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A. A
B. B
C. C
D. D
A. 210 adult; 120 children
B. 120 adult; 210 children
C. 300 children; 30 adult
D. 300 children; 30 adult
AMUSEMENT PARKS At Amy’s Amusement Park, tickets sell for $24.50 for adults and $16.50 for children. On Sunday, the amusement park made $6405 from selling 330 tickets. How many of each kind of ticket was sold?
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Solve by Using Elimination
Use the elimination method to solve the system of equations.
x + 2y = 10x + y = 6
In each equation, the coefficient of x is 1. If one equation is subtracted from the other, the variable x will be eliminated.
x + 2y = 10
(–)x + y = 6
y = 4 Subtract the equations.
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Solve by Using Elimination
Now find x by substituting 4 for y in either original equation.
x + y = 6 Second equation
x + 4 = 6 Replace y with 4.
x = 2 Subtract 4 from each side.
Answer: The solution is (2, 4).
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A. A
B. B
C. C
D. D
A. (2, –1)
B. (17, –4)
C. (2, 1)
D. no solution
Use the elimination method to solve the system of equations. What is the solution to the system?x + 3y = 5x + 5y = –3
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Read the Test ItemYou are given a system of two linear equations and are asked to find the solution.
Solve the system of equations.2x + 3y = 125x – 2y = 11
A. (2, 3)
B. (6, 0)
C. (0, 5.5)
D. (3, 2)
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x = 3
Multiply the first equation by 2 and the second equation by 3. Then add the equations to eliminate the y variable.
2x + 3y = 12 4x + 6y = 24Multiply by 2.
Multiply by 3.
5x – 2y = 11 (+)15x – 6y = 3319x = 57
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Replace x with 3 and solve for y.
2x + 3y = 12 First equation
2(3) + 3y = 12 Replace x with 3.
6 + 3y = 12 Multiply.
3y = 6 Subtract 6 from each side.
y = 2 Divide each side by 3.
Answer: The solution is (3, 2). The correct answer is D.
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A. A
B. B
C. C
D. D
Solve the system of equations.x + 3y = 72x + 5y = 10
A.
B. (1, 2)
C. (–5, 4)
D. no solution
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No Solution and Infinite Solutions
A. Use the elimination method to solve the system of equations.–3x + 5y = 126x – 10y = –21
Use multiplication to eliminate x.
–3x + 5y = 12 –6x + 10y = 24Multiply by 2.
0 = 3
6x – 10y = –21 (+)6x – 10y = –21
Answer: Since there are no values of x and y that will make the equation 0 = 3 true, there are no solutions for the system of equations.
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No Solution and Infinite Solutions
B. Use the elimination method to solve the system of equations.–3x + 4y = 79x – 12y = –21
Use multiplication to eliminate x.
–3x + 4y = 7 –9x + 12y = 21Multiply by 3.
0 = 0
9x – 12y = –21 (+)9x – 12y = –21
Answer: Because the equation 0 = 0 is always true, there are an infinite number of solutions.
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A. A
B. B
C. C
D. D
A. (1, 3)
B. (–5, 0)
C. (2, –2)
D. no solution
Use the elimination method to solve the system of equations. What is the solution to the system of equations?2x + 3y = 11–4x – 6y = 20