Equations as RelationsBy: 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 VocabularyEquation 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 SetReplacement 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)}
x y -3x+y=7-5 0 -3 -2
-3(-5)+(0)=7 15 = 7-3(-3)+(-2)=7 7=7
Solve -3x+y=7 if the replacement set is {(-5,0),(-3,-2),(2,13),(4,19)}
x y -3x+y=7 2 13 4 19
-3(2)+(13)=7 7=7-3(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 y9 3 15x y 9x 9x
3 9 15y x 3 9 153 3y x
3 5y x
Solve 9x+3y=15 if the domain is { 0,1,2,3}
x y=-3x+50
1
y=-3(0)+5y
y=-3(1)+5
= 5
= 2
Solve 9x+3y=15 if D={ 0,1,2,3}
x y=-3x+501
y=-3(0)+5y
y=-3(1)+5= 5= 2
2
y=-3(2)+5 = -13
y=-3(3)+5 = -4
Sol. Set={(0,5),(1,2),(2,-1),(3,-4)|