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Graphing Method
Graphing Method
Solve the following system of equations using the Graphing Method.
- y = -2x + 3
- 3y + 2x = 4
Answer: (1, 1)
Substitution Method
Substitution Method
Solve the following system of equations using the Substitution Method.
- y = -2x + 3
- 3y + 2x = 4
3(-2x + 3) + 2x = 4
-6x + 9 + 2x = 4
-4x = -4
x = 1
y = -2(1) +3
y = 1
Answer: (1, 1)
Elimination Method
Elimination Method
Solve the following system of equations using the Elimination Method.
- y = -2x + 3
- 3y + 2x = 4
y + 2x = 3
2y + 2x = 4
(y - 2y) + (2x - 2x) = (3 - 4)
(-y) + (0) = (-1)
y = 1
1 + 2x = 3
2x = 2
x = 1
Answer: (1, 1)
Tickets to a carnival are $5 for adults and $3 for children. If 251 people attended and the [total ticket sales] were $925, how many tickets were bought for children?
5a + 3c = 925
a + c = 251
Answer: 165 children tickets
Scalar Multiplication and Addition of Matrices
Scalar Multiplication and Addition of Matrices
Multiply and add.
Multiplying Matrices
Multiplying Matrices
Multiply.
(3 x 2) (2 x 3) - the columns of the first matrix and the rows of the second match, so yes, the matrices will multiply.
(3 x 2) (2 x 3) - the product will be a 3 x 3 matrix.
Multiplying Matrices (DNE)
Multiplying Matrices (DNE)
Multiply.
(2 x 2) (3 x 3) - the columns of the first matrix and the rows of the second do not match, so no, the matrices will not multiply.
Answer: DNE
Determinant
Determinant
Example: find the determinant of the matrix.
Inverse
Inverse
Example: find the determinant of the matrix.
Solving Matrix Equations
Solving Matrix Equations
Solve for Matrix A.
Systems of Equations using Matrix Method (2x2)
Systems of Equations using Matrix Method (2x2)
Solve the system of equation using matrices.
(3, 0)
Systems of Equations using Matrix Method (3x3)
Systems of Equations using Matrix Method (3x3)
Solve the system of equation using matrices.
x = -6, y = 6, z = 5
Applications of Systems of Equations (2x2)
Applications of Systems of Equations (2x2)
2s + 7t = 154
11s + 4t = 157
Small: $7
Large: $20
Applications of Systems of Equations (3x3)
Applications of Systems of Equations (3x3)
5x + y + 18z = 86
x + y + z = 20
x - y + z = 0
8 cakes, 10 eggs, 2 pizzas
Systems of Inequalities
Systems of Inequalities
Solve the following inequalities by graphing the solution.
y>=2x-3
y>-3x+2
Linear Programming
Linear Programming
(0, 45) - $1350
(30, 15) - $1650
(36, 0) - $1400
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