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
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 The simplest linear system is one with two equations and two variables.
Graph of a Linear Equation
Graph of y = 3x – 2
x y
1 1
0 -2
-1 -5
Graph of a Linear Equation
Graph of y = –x – 6
x y
1 -7
0 -6
-1 -5
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
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)
Practice Solving Systems of Linear Equations
Solve by Graphing the following systems of linear equations (see worksheet #1):#1
Practice Solving Systems of Linear Equations
Solve by Graphing the following systems of linear equations (see worksheet #1):#2
Practice Solving Systems of Linear Equations
Solve by Graphing the following systems of linear equations (see worksheet #1):#3
Practice Solving Systems of Linear Equations
Solve by Graphing the following systems of linear equations (see worksheet #1):#4
Practice Solving Systems of Linear Equations
Solve by Graphing the following systems of linear equations (see worksheet #1):#5
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
Solving Systems of Linear Equations
Substitution Method:2x – 3y = –24x + y = 24
Simplify: 2x – 72 + 12x = –2 14x – 72 = -2
14x = 70 x = 5
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
Solving Systems of Linear Equations
Substitution Method:2x – 3y = –24x + y = 24
The solution is the ordered pair (5, 4).
Practice Solving Systems of Linear Equations
Solve by Substitution the following systems of linear equations (see worksheet #2):#1
Practice Solving Systems of Linear Equations
Solve by Substitution the following systems of linear equations (see worksheet #2):#2
Practice Solving Systems of Linear Equations
Solve by Substitution the following systems of linear equations (see worksheet #2):#3
Practice Solving Systems of Linear Equations
Solve by Substitution the following systems of linear equations (see worksheet #2):#4
Practice Solving Systems of Linear Equations
Solve by Substitution the following systems of linear equations (see worksheet #2):#5
Solving an Equation
Addition or Elimination Method:
Example: x + 6 = 11 -6 -6 x = 5
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
Solving Systems of Linear Equations
Addition or Elimination Method - easy:2x + y = 9
3x – y = 16
Solution is (5, -1)
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
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
Solving Systems of Linear Equations
Addition or Elimination Method – medium:2x – y = 9
3x + 4y = –14
Solution is (2, -5)
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
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)
Practice Solving Systems of Linear Equations
Solve by Addition/Elimination the following systems of linear equations (see worksheet #3):#1
Practice Solving Systems of Linear Equations
Solve by Addition/Elimination the following systems of linear equations (see worksheet #3):#2
Practice Solving Systems of Linear Equations
Solve by Addition/Elimination the following systems of linear equations (see worksheet #3):#3
Practice Solving Systems of Linear Equations
Solve by Addition/Elimination the following systems of linear equations (see worksheet #3):#4
Practice Solving Systems of Linear Equations
Solve by Addition/Elimination the following systems of linear equations (see worksheet #3):#5