systems of linear equations
DESCRIPTION
Systems of Linear Equations. Block 44. System of Linear Equations. A system of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/1.jpg)
Systems of Linear Equations
Block 44
![Page 2: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/2.jpg)
System of Linear Equations
A system of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations The simplest linear system is one with two equations and two variables.
![Page 3: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/3.jpg)
Graph of a Linear Equation
Graph of y = 3x – 2
x y
1 1
0 -2
-1 -5
![Page 4: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/4.jpg)
Graph of a Linear Equation
Graph of y = –x – 6
x y
1 -7
0 -6
-1 -5
![Page 5: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/5.jpg)
System of Linear Equations
Graph of y = 3x – 2 & y = –x – 6x y
1 1
0 -2
-1 -5
x y
1 -7
0 -6
-1 -5
![Page 6: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/6.jpg)
System of Linear Equations
Graph of y = 3x – 2 & y = –x – 6x y
1 1
0 -2
-1 -5
x y
1 -7
0 -6
-1 -5
Solution is (-1, -5)
![Page 7: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/7.jpg)
Practice Solving Systems of Linear Equations
Solve by Graphing the following systems of linear equations (see worksheet #1):#1
![Page 8: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/8.jpg)
Practice Solving Systems of Linear Equations
Solve by Graphing the following systems of linear equations (see worksheet #1):#2
![Page 9: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/9.jpg)
Practice Solving Systems of Linear Equations
Solve by Graphing the following systems of linear equations (see worksheet #1):#3
![Page 10: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/10.jpg)
Practice Solving Systems of Linear Equations
Solve by Graphing the following systems of linear equations (see worksheet #1):#4
![Page 11: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/11.jpg)
Practice Solving Systems of Linear Equations
Solve by Graphing the following systems of linear equations (see worksheet #1):#5
![Page 12: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/12.jpg)
Solving Systems of Linear Equations
Substitution Method:2x – 3y = –24x + y = 24
Choose 2nd equation: 4x + y = 24 Rewrite with single variable: y = 24 – 4xSubstitute into 1st equation: 2x – 3(24 – 4x) = –2
![Page 13: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/13.jpg)
Solving Systems of Linear Equations
Substitution Method:2x – 3y = –24x + y = 24
Simplify: 2x – 72 + 12x = –2 14x – 72 = -2
14x = 70 x = 5
![Page 14: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/14.jpg)
Solving Systems of Linear Equations
Substitution Method:2x – 3y = –24x + y = 24
Substitute x = 5 into either equation: 4x + y = 24 4(5) + y = 24 20 + y = 24y = 24 – 20y = 4
![Page 15: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/15.jpg)
Solving Systems of Linear Equations
Substitution Method:2x – 3y = –24x + y = 24
The solution is the ordered pair (5, 4).
![Page 16: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/16.jpg)
Practice Solving Systems of Linear Equations
Solve by Substitution the following systems of linear equations (see worksheet #2):#1
![Page 17: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/17.jpg)
Practice Solving Systems of Linear Equations
Solve by Substitution the following systems of linear equations (see worksheet #2):#2
![Page 18: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/18.jpg)
Practice Solving Systems of Linear Equations
Solve by Substitution the following systems of linear equations (see worksheet #2):#3
![Page 19: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/19.jpg)
Practice Solving Systems of Linear Equations
Solve by Substitution the following systems of linear equations (see worksheet #2):#4
![Page 20: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/20.jpg)
Practice Solving Systems of Linear Equations
Solve by Substitution the following systems of linear equations (see worksheet #2):#5
![Page 21: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/21.jpg)
Solving an Equation
Addition or Elimination Method:
Example: x + 6 = 11 -6 -6 x = 5
![Page 22: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/22.jpg)
Solving Systems of Linear Equations
Addition or Elimination Method-easy:2x + y = 9
3x – y = 16
Add: 5x = 25Simplify: x = 5Substitute: 2(5) + y = 9
10 + y = 9 y = -1
![Page 23: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/23.jpg)
Solving Systems of Linear Equations
Addition or Elimination Method - easy:2x + y = 9
3x – y = 16
Solution is (5, -1)
![Page 24: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/24.jpg)
Solving Systems of Linear Equations
Addition or Elimination Method – medium:2x – y = 9
3x + 4y = –14
Multiply 1st by 4: 8x – 4y = 36
8x – 4 y = 363x + 4y = –14
![Page 25: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/25.jpg)
Solving Systems of Linear Equations
Addition or Elimination Method – medium:8x – 4 y = 36
3x + 4y = –14
Multiply 1st by 4: 8x – 4y = 36Add: 11x = 22Simplify: x = 2Substitute: 2(2) – y = 9
4 – y = 9 -y = 5 or y = -5
![Page 26: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/26.jpg)
Solving Systems of Linear Equations
Addition or Elimination Method – medium:2x – y = 9
3x + 4y = –14
Solution is (2, -5)
![Page 27: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/27.jpg)
Solving Systems of Linear EquationsAddition or Elimination Method – hard:
4x – 3y = 25 –3x + 8y = 10
Multiply 1st by 3: 12x – 9y = 75Multiply 2nd by 4: -12x + 32y = 40
![Page 28: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/28.jpg)
Solving Systems of Linear EquationsAddition or Elimination Method – hard:
12x – 9y = 75-12x + 32y = 40
Add: 23y = 115Simplify: y = 5Substitute (original equation) : 4x – 3y = 25
4x – 3(5) = 25 4x = 40x = 10
Solution is (10, 5)
![Page 29: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/29.jpg)
Practice Solving Systems of Linear Equations
Solve by Addition/Elimination the following systems of linear equations (see worksheet #3):#1
![Page 30: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/30.jpg)
Practice Solving Systems of Linear Equations
Solve by Addition/Elimination the following systems of linear equations (see worksheet #3):#2
![Page 31: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/31.jpg)
Practice Solving Systems of Linear Equations
Solve by Addition/Elimination the following systems of linear equations (see worksheet #3):#3
![Page 32: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/32.jpg)
Practice Solving Systems of Linear Equations
Solve by Addition/Elimination the following systems of linear equations (see worksheet #3):#4
![Page 33: Systems of Linear Equations](https://reader035.vdocuments.site/reader035/viewer/2022062502/56813a32550346895da21c5d/html5/thumbnails/33.jpg)
Practice Solving Systems of Linear Equations
Solve by Addition/Elimination the following systems of linear equations (see worksheet #3):#5