2 Variables
Solve for x and y using combination:
5x + 2y = 11
x + y = 4
{(1,3)}
What are the two processes we use to solve a system with three variables?
Combination (or elimination) and Determinants (or Matrices), Diagonal Method
Use determinants to solve the system of equations:
x - y = -11
7x + 4y = -22
{(-6, 5)}
How do you say f(x) - write it on your boards
f of x
What is a set of open sentences each of which contains the same variables.
System
What is your favorite class in school
Math, duh!
Solve for x and y:
2x + 3y = 2
4x - 9y = -1
{(1/2, 1/3)}
How many axis does a system with three equations have?
3
Find the Denominator Determinant:
3x + 4y + 2z = 6
x + 3y - 5z = -7
5x + 7y - 3z = 3
-26
f(x) = 3x + 11
g(x) = x2 + x + 1
Find f(7)
32
What is the set of all ordered pairs that satisfy all the open sentences in the system.
Solution Set
What are the names of Mrs. Callen's 3 kids?
Rush, Cooper, and Emmaline
Solve for x and y
11x - 5y = -38
9x + 2y = -25
{(-3, 1)}
Solve for x:
x - 2y + 3z = 3
2x + y + 5z = 8
3x - y - 3z = -22
x = -4
Find the x Determinant: The denominator determinant is -26
3x + 4y + 2z = 6
x + 3y - 5z = -7
5x + 7y - 3z = 3
-104
f(x) = 3x + 11
g(x) = x2 + x + 1
Find g(-3)
7
What is a square array of numbers that is expanded (evaluated) according to the rule?
Second Order Determinant (or matrix)
What is the rule called that we follow to solve determinants?
Cramer's rule
Solve for x and y
12x - 7y = 59
8x + 11y = -39
{(2, -5)}
Solve for y: x = -4
x - 2y + 3z = 3
2x + y + 5z = 8
3x - y - 3z = -22
y = 1
Find the y Determinant: The denominator is -26
3x + 4y + 2z = 6
x + 3y - 5z = -7
5x + 7y - 3z = 3
52
g( f ( -5 ))
13
Which variable does the symbol f(x) represent?
y or dependent variable
It's April Fools and you decide to play a trick on your family. You have 4 salt shakers and you replace 3 of them with sugar. You leave these messages on each of them:
Shaker A: This is salt
Shaker B: This is salt
Shaker C: This is sugar
Shaker D: The salt is not in B
If only one message is true, which shaker contains salt?
Shaker C
Solve for x and y:
18x - 19y = 161
54x + 25y = 565
{(10, 1)}
Solve for z: x = -4 and y = 1
x - 2y + 3z = 3
2x + y + 5z = 8
3x - y - 3z = -22
z = 3
Find the z Determinant: The denominator is -26
3x + 4y + 2z = 6
x + 3y - 5z = -7
5x + 7y - 3z = 3
-26 (4, -2, 1)
f(x) = 3x + 11
g(x) = x2 + x + 1
f ( g ( x ))
3x2 + 3x + 14
Describe what an intercept is on a graph.
The value of x when y is 0 or vice versa.
f(x) = 3x + 11
g(x) = x2 + x + 1
Find g ( g ( x ))
x4 + 2x3 + 4x2 + 3x + 3