Equations as Relations Lesson for Glencoe Algebra I Math By: Cathy Miller Bartlett High School Lesson for Glencoe Algebra I Math Section 4-4 Algebra I Glencoe Mathematics 2004 The McGraw Hill Companies Inc.

Ways to write a relation Set of ordered pairs Table Mapping Graph Equation in two variables

New Vocabulary Equation in Two Variables – Equations with 2 different variables. Solution to Equation in Two Variables – any point that makes a true statement when you substitute the x and y values into the equation.

Solve Using a Replacement Set Replacement set = a set of possible solutions. Substitute the points to find the true solutions… these are the ones that make the equation true. Solution set = the set of true solutions.

Solve -3x+y=7 if the replacement set is {(-5,0),(-3,-2),(2,13),(4,19)} -5 0 -3(-5)+(0)=7 15 = 7 -3 -2 -3(-3)+(-2)=7 7=7

Solve -3x+y=7 if the replacement set is {(-5,0),(-3,-2),(2,13),(4,19)} 2 13 -3(2)+(13)=7 7=7 4 19 -3(4)+(19)=7 7=7

Solve y=7+3x if the replacement set is {(-5,0),(-3,-2),(2,13),(4,19)} Solution set = {(-3,-2),(2,13),(4,19)}

Solve Using a Given Domain Domain = the x’s for your solution setlthat you can use Substitute the x’s to find their y’s. Solution set = the set (x,y)’s

Solve 9x+3y=15 if the domain is { 0,1,2,3} First…solve the equation for y

Solve 9x+3y=15 if the domain is { 0,1,2,3} y=-3x+5 y y=-3(0)+5 = 5 1 y=-3(1)+5 = 2

x y y=-3x+5 y=-3(0)+5 = 5 1 y=-3(1)+5 = 2 2 y=-3(2)+5 = -1 3 y=-3(3)+5 Solve 9x+3y=15 if D={ 0,1,2,3} x y y=-3x+5 y=-3(0)+5 = 5 1 y=-3(1)+5 = 2 2 y=-3(2)+5 = -1 3 y=-3(3)+5 = -4 Sol. Set={(0,5),(1,2),(2,-1),(3,-4)|