1. 9.3 Equations as Relations CORD Math Mrs. Spitz Fall 2006

2. Objectives: Solve linear equations for a specific variable, and Solve linear equations for a given domain Whats linear?

3. Assignment Pgs. 367 -368 #4 – 41 all

4. Definition of the solution of an equation in two variables If a true statement results when the numbers in an ordered pair are substituted into an equation in two variables, then the ordered pair is a solution of the equation

5. More Since the solutions of an equation in two variables are ordered pairs, such an equation describes a relation. The set of values of x is the domain of the relation. The set of corresponding values of y is the range of the relation.

6. Ex. 1: Solve y = 2x +3 if the domain is {-5, -3, -1, 0, 1, 3, 5, 7, 9} x2x + 3y(x, y) -52(-5) + 3 = -10 + 3 = -7-7(-5, -7) -32(-3) +3 = -6 + 3 = -3-3(-3, -3) 2(-1) + 3 = -2 + 3 = 11(-1, 1) 02(0) + 3 = 0 + 3 = 33(0, 3) 12(1) + 3 = 2 + 3 = 55(1, 5) 32(3) + 3 = 6 + 3 = 99(3, 9) 52(5) + 3 = 10 + 3 = 1313(5, 13) 72(7) + 3 = 14 + 3 = 1717(7, 17) 92(9) + 3 = 18 + 3 = 2121(9, 21) The solution set is (x, y) column

7. Ex. 2: Solve 3y + 6x = 12 if the domain is {-4, -3, -2, 2, 3, 4} x-2x + 4y(x, y) -4-2(-4) + 4 = 8 + 4 = 1212(-4, 12) -3-2(-3) +4 = 6 + 4 = 1010(-3, 10) -2-2(-2) + 4 = 4 + 4 = 88(-2, 8) 2-2(2) + 4 = -4 + 4 = 00(2, 0) 3-2(3) + 4 = -6 + 4 = -2-2(3, -2) 4-2(4) + 4 = -8 + 4 = -4-4(4, -4) The solution set is (x, y) column First solve for y: 3y + 6x = 12 3y = -6x + 12 y = -2x + 4

8. Homework problems #4,5 are table of values to complete #6-8/13-15 are multiple choice. #9-12/16-23 are solve for the variable indicated #24-41 are given that domain is, then solve each equation for the range. You need a ruler to make tables or be careful making them.