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Open Sentences in 2 Variables 3-1 Open Sentence: An equation or inequality that has one or more variables Open sentences in 2 variables look like: x+y=5 x + 2y < 4 We’re solving these kind today 2 y = x + 5x - 3 The Solution Set of an Open Sentence in 2 Variables is: An ordered pair (x, y) The X values are called the Domain (you may be given these values) The Y values are called the Range (you get the y values after you plug in x) 1 Example: Solve the equation if the domain of x is: {0, 1, 2} Procedure: 3x – 2y = 7 1. Solve for y (get y by itself) EAT REP ALL FOR N X GIVE ES U VAL ain) m (d o 2. Substitute in x value (domain) 3. Get y (range) value Another type of Problem: Complete each ordered pair to form a solution. 2x +3y = 12 given: (0,__),( __, 0) Need to find Y Need to find X Procedure: 1. Plug in given value into equation 2. Solve for missing variable (All you are doing is substituting) Another Example: A customer asks a bank teller for $390 in travelers checks, some are worth $50, some are worth $20. Find all possibilities for the number of each type of check the customer could receive. 2 Procedure: 1. Re-read: What is the problem asking for ? 2. Set up variables let x = # of 50’s let y = # of 20’s 3. Set up equation 50x +20y = 390 4. Solve for y 5. Find X values –X in this problem must be a positive whole number Another type! Find the value of k so that the ordered pair satisfies the equation. 3x – y = k; (-1, 3) Procedure: 1. Plug in ordered pair into equation 2. Solve for k 3