Download Open Sentences in Two Variables

Open Sentences
(two variables)
Open Sentences in Two Variables
Open Sentence
Solution
Equations or inequalities which contain two variables.
9x + 2y = 15 2x ­ y > 6
In an open sentence, the two variable pairs, x & y, that make the sentence true are called solutions.
4x + 2y = 24
Ordered Pair
Solutions for open sentences are usually written in the form ( x , y ) called an ordered pair.
The solution above:
Solution Set
Solving
Domain
Range
x = 3 & y = 6 is a solution
( 3 , 6 )
The set of all ordered pairs that make an open sentence true. This set is sometimes infinite.
Finding the solution set of an open sentence is called solving.
All of the "x" values also known as the input or independent variable.
All of the "y" values also known as the output or dependent variable.
Open Sentences in Two Variables
Example 1)
Solve the equation 9x + 2y = 15 if the domain of x is {­1, 0, 1, 2, 3}:
Solution Set:
(­1 , ) ( 0 , ) ( 1 , ) ( 2 , ) ( 3 , )
Open Sentences in Two Variables
Example 2)
A customer asks a bank teller for $390 in traveler's checks, some worth $50 and some worth $20. Find all Possibilities for the number of each type of check the customer could receive.
Let f = the number of $50 checks and Let t = the number of $20 checks
Open Sentences in Two Variables
Example 3)
Find all positive two­digit odd numbers with this property: When the digits are interchanged, the results exceeds the original number by more than 36.
Let u = the units' digit and Let t = the tens' digit.
Open Sentences in Two Variables
Example 4)
Find the value of k so that the ordered pair satisfies the equation.
3x ­ ky = 4; ( 2, ­1 )