Equations as Relations
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
•
•
•
•
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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)}
x
-5
-3
y
0
-3x+y=7
-3(-5)+(0)=7
15 = 7
-2 -3(-3)+(-2)=7
7=7
Solve -3x+y=7 if the replacement set
is {(-5,0),(-3,-2),(2,13),(4,19)}
x
2
4
y
13
-3x+y=7
-3(2)+(13)=7
7=7
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
9x  3y  15
9x
9x
3y  9
9x  15

3
3
y  3x  5
Solve 9x+3y=15 if the domain is
{ 0,1,2,3}
x
0
y=-3x+5
y=-3(0)+5
y
= 5
1
y=-3(1)+5
= 2
Solve 9x+3y=15 if D={ 0,1,2,3}
x
0
1
2
3
y=-3x+5
y=-3(0)+5
y=-3(1)+5
y=-3(2)+5
y=-3(3)+5
y
= 5
= 2
= -1
= -4
Sol. Set={(0,5),(1,2),(2,-1),(3,-4)|