algebra 1 notes lesson 7-4 elimination using multiplication
TRANSCRIPT
![Page 1: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/1.jpg)
Algebra 1 Notes
Lesson 7-4
Elimination Using Multiplication
![Page 2: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/2.jpg)
Mathematics Standards- Number, Number Sense and Operations:
Explain the effects of operations such as multiplication or division, and of computing the powers and roots on the magnitude of quantities.
- Patterns, Functions and Algebra: Add, subtract, multiply and divide monomials and polynomials.
- Patterns, Functions and Algebra: Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.
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Mathematics Standards- Patterns, Functions and Algebra: Solve and
interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.
- Patterns, Functions and Algebra: Solve real world problems that can be modeled using systems of linear equations and inequalities.
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Elimination with Multiplication
One more
step than before
![Page 5: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/5.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23
3x + 2y = 37
multiply by 2
![Page 6: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/6.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37
![Page 7: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/7.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37 keep the same
![Page 8: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/8.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37 3x + 2y = 37
![Page 9: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/9.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37 (–) 3x + 2y = 37
x = 9
![Page 10: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/10.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37 (–) 3x + 2y = 37
x = 9
![Page 11: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/11.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37 (–) 3x + 2y = 37
3(9) + 2y = 37 x = 9 .
![Page 12: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/12.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37 (–) 3x + 2y = 37
3(9) + 2y = 37 x = 9
27 + 2y = 37
![Page 13: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/13.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37 (–) 3x + 2y = 37
3(9) + 2y = 37 x = 9
27 + 2y = 37 – 27 – 27
![Page 14: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/14.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37 (–) 3x + 2y = 37
3(9) + 2y = 37 x = 9
. 27 + 2y = 37 – 27 – 27
2y = 10
![Page 15: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/15.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37 (–) 3x + 2y = 37
3(9) + 2y = 37 x = 9
27 + 2y = 37 – 27 – 27
2y = 10 2 2
![Page 16: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/16.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37 (–) 3x + 2y = 37
3(9) + 2y = 37 x = 9
27 + 2y = 37 – 27 – 27
2y = 10 2 2 y = 5
![Page 17: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/17.jpg)
Example 1Use elimination to solve the system of equations.
2x +y = 23 multiply by 2 4x + 2y = 46
3x + 2y = 37 (–) 3x + 2y = 37
3(9) + 2y = 37 x = 9
27 + 2y = 37 – 27 – 27 (9, 5)
2y = 10 2 2 y = 5
![Page 18: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/18.jpg)
Example 2Use elimination to solve the system of equations.
4x + 3y = 8
3x – 5y = -23
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Example 2Use elimination to solve the system of equations.
4x + 3y = 8 multiply by 3
3x – 5y = -23
![Page 20: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/20.jpg)
Example 2Use elimination to solve the system of equations.
4x + 3y = 8 multiply by 3 12x + 9y = 24
3x – 5y = -23
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Example 2Use elimination to solve the system of equations.
4x + 3y = 8 multiply by 3 12x + 9y = 24
3x – 5y = -23 multiply by 4
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Example 2Use elimination to solve the system of equations.
4x + 3y = 8 multiply by 3 12x + 9y = 24
3x – 5y = -23 multiply by 4 12x – 20y = -92
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Example 2Use elimination to solve the system of equations.
4x + 3y = 8 multiply by 3 12x + 9y = 24
3x – 5y = -23 multiply by 4 (-)12x – 20y = -92
29y = 116
29 29
y = 4
![Page 24: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/24.jpg)
Example 2Use elimination to solve the system of equations.
4x + 3y = 8 multiply by 3 12x + 9y = 24
3x – 5y = -23 multiply by 4 (-)12x – 20y = -92
29y = 116
29 29
y = 4
![Page 25: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/25.jpg)
Example 2Use elimination to solve the system of equations.
4x + 3y = 8 multiply by 3 12x + 9y = 24
3x – 5y = -23 multiply by 4 (-)12x – 20y = -92
3x – 5(4) = -23 29y = 116
29 29
y = 4
![Page 26: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/26.jpg)
Example 2Use elimination to solve the system of equations.
4x + 3y = 8 multiply by 3 12x + 9y = 24
3x – 5y = -23 multiply by 4 (-)12x – 20y = -92
3x – 5(4) = -23 29y = 116
3x – 20 = -23 29 29
y = 4
![Page 27: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/27.jpg)
Example 2Use elimination to solve the system of equations.
4x + 3y = 8 multiply by 3 12x + 9y = 24
3x – 5y = -23 multiply by 4 (-)12x – 20y = -92
3x – 5(4) = -23 29y = 116
3x – 20 = -23 29 29
+20 +20 y = 4
3x = -3
3 3
![Page 28: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/28.jpg)
Example 2Use elimination to solve the system of equations.
4x + 3y = 8 multiply by 3 12x + 9y = 24
3x – 5y = -23 multiply by 4 (-)12x – 20y = -92
3x – 5(4) = -23 29y = 116
3x – 20 = -23 29 29
+20 +20 y = 4
3x = -3
3 3 x = -1
![Page 29: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/29.jpg)
Example 2Use elimination to solve the system of equations.
4x + 3y = 8 multiply by 3 12x + 9y = 24
3x – 5y = -23 multiply by 4 (-)12x – 20y = -92
3x – 5(4) = -23 29y = 116
3x – 20 = -23 29 29
+20 +20 y = 4
3x = -3
3 3 x = -1 (-1, 4)
![Page 30: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/30.jpg)
Example 3Determine the best method to solve the system of equations. Then solve the system.
x + 5y = 4
3x – 7y = -10
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Example 3
Three Options:
Graphing – Rarely best
Substitution – If variable is solved for
or easily solved for
Elimination – If variable has same coefficient
or solving for a variable gives a fraction
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Example 3Determine the best method to solve the system of equations. Then solve the system.
x + 5y = 4
3x – 7y = -10
The best method to use is substitution because the coefficient of x in the first equation is 1, which makes it easy to solve for.
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Example 3 x + 5y = 4 3x – 7y = -10
– 5y – 5y
x = 4 – 5y
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Example 3 x + 5y = 4 3x – 7y = -10
– 5y – 5y
x = 4 – 5y
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Example 3 x + 5y = 4 3x – 7y = -10
– 5y – 5y 3(4 – 5y) – 7y = -10
x = 4 – 5y
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Example 3 x + 5y = 4 3x – 7y = -10
– 5y – 5y 3(4 – 5y) – 7y = -10
x = 4 – 5y
![Page 37: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/37.jpg)
Example 3 x + 5y = 4 3x – 7y = -10
– 5y – 5y 3(4 – 5y) – 7y = -10
x = 4 – 5y 12 – 15y – 7y = -10
12 – 22y = -10
– 12 – 12
-22y = -22
-22 -22
y = 1
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Example 3 x + 5y = 4 3x – 7y = -10
– 5y – 5y 3(4 – 5y) – 7y = -10
x = 4 – 5y 12 – 15y – 7y = -10
12 – 22y = -10
– 12 – 12
-22y = -22
-22 -22
y = 1
![Page 39: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/39.jpg)
Example 3 x + 5y = 4 3x – 7y = -10
– 5y – 5y 3(4 – 5y) – 7y = -10
x = 4 – 5y 12 – 15y – 7y = -10
x = 4 – 5(1) 12 – 22y = -10
– 12 – 12
-22y = -22
-22 -22
y = 1
![Page 40: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/40.jpg)
Example 3 x + 5y = 4 3x – 7y = -10
– 5y – 5y 3(4 – 5y) – 7y = -10
x = 4 – 5y 12 – 15y – 7y = -10
x = 4 – 5(1) 12 – 22y = -10
x = 4 – 5 – 12 – 12
-22y = -22
-22 -22
y = 1
![Page 41: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/41.jpg)
Example 3 x + 5y = 4 3x – 7y = -10
– 5y – 5y 3(4 – 5y) – 7y = -10
x = 4 – 5y 12 – 15y – 7y = -10
x = 4 – 5(1) 12 – 22y = -10
x = 4 – 5 – 12 – 12
x = -1 -22y = -22
-22 -22
y = 1
![Page 42: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/42.jpg)
Example 3 x + 5y = 4 3x – 7y = -10
– 5y – 5y 3(4 – 5y) – 7y = -10
x = 4 – 5y 12 – 15y – 7y = -10
x = 4 – 5(1) 12 – 22y = -10
x = 4 – 5 – 12 – 12
x = -1 -22y = -22
(-1, 1) -22 -22
y = 1
![Page 43: Algebra 1 Notes Lesson 7-4 Elimination Using Multiplication](https://reader035.vdocuments.us/reader035/viewer/2022062517/56649f145503460f94c2951c/html5/thumbnails/43.jpg)
Homework
Pg. 391
14-38 evens