Definitions
Substitution
Elimination
Matrices
OTHER
100
What is a 'system of equations'?
Two or more equations that are to be solved at the same time form a system of equations
100
7x - 2y = -2 y=3x
(-2, -6)
100
3x - y = -7 2x + y = -3
(-2, 1)
100
Put this system into an augmented matrix (do not solve) 3x - y - z = -8 4x + 2y + 3z = 15 -6x + 2y + 2z = 10
3 -1 -1 | -8 4 2 3 | 15 -6 2 2 | 10
100
What is an ordered triple?
(x, y, z)
200
What is a linear system?
A linear system is a system of equations that contains only linear equations
200
5x - 3y = -6 x = 2 - y
(0,2)
200
-2x + 3y = -10 2x + 2y = 5
(7/2 , -1)
200
What are the 3 permitted row operations? (We use these to put an augmented matrix into row echelon form)
1. Multiply a row by a constant 2. Interchange one row with another (switch the order) 3. Add two rows together
200
Solve the system in any way: 4x + 8y + z = 2 x + 7y = 3z = -14 2x - 3y + 2z = 3
(-3, 1, 6)
300
what is a Consistent system? an inconsistent system?
A system is consistent if it has a solution. A system is inconsistent if it has no solution
300
3x - y = 10 2x + 5y = 1
(3, -1)
300
x + 3y = 8 2x - 5y = -17
(-1, 3)
300
Solve using row operations: 6x + 3y = 9 -7x + 2y = 17
(-1, 5)
300
Without doing any algebra, explain why the following system has no solution y = 3x + 2 y = 3x - 4
Looking at the graphs of the two lines, they are parallel. Also, the two equations are already in slope intercept form. Identifying the slope of each line, it can be seen that they are equal. Therefore, the lines never intersect... which means the system has no solution!
400
What is an augmented matrix?
An augmented matrix is a matrix that has a vertical bar that separates the columns of the matrix into two groups. (We have said this line represents the 'equal' sign)
400
-2x + 5y = 22 1/2x + 1/4y = 1/2
(-1, 4)
400
6x - 2y = -21 -3x + 4y = 36
(-2/3 , 17/2)
400
Solve using a matrix: x + 2y - z = 1 3x + 4y + 2z = -2 -2x - y + x = -1
(0, 0, 1)
400
A local electronics store will sell AC adaptors and 2 rechargeable flashlights for $86, or 3 AC adaptors and 4 rechargeable flashlights for $84. What is the price of a single AC adaptor and a single rechargeable flashlight?
AC adaptor: $8 Rechargeable flashlight: $15
500
What is row echelon form?
If a matrix is written with 1's down the diagonal from upper left to lower right and 0's below the 1's, it is said to be in row echelon form
500
1/5x + 2/3y = -8/5 3x - y = 9
(2, -3)
500
2x + 3y - z = -16 x + 2y + 2z = -3 -3x + y + z = -5
(1, -5, 3)
500
Solve using a matrix: x + 3y + 2z = 11 3x + 7y + 4z = 23 5x + 3y - 5z = -14
What is (-1, 2, 3)
500
The owner of a tea shop wants to mix three kinds of tea to make 100 ounces of a mixture that will sell for $0.83 per ounce. He uses Orange Pekoe, which sells for $0.80 per ounce, Irish Breakfast, for $0.85 per ounce, and Earl Grey, for $0.95 per ounce. If he wants to use twice as much Orange pekoe as Irish breakfast, how much of each kind should he use?
Orange Pekoe - 60 Ounces Irish breakfast - 30 ounces Earl Grey - 10 ounces
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