Systems of Equations
Mathematics 17
Institute of Mathematics, University of the PhilippinesDiliman
Lecture 12
Math 17
(UPIMath)
Systems
Lec 12
1 / 29
Outline
1
Two Linear Equations in Two Variables
2
Examples of Systems Involving Quadratic Equations
A Line and a Parabola
A Line and a Circle
3
Three Linear Equations in Three variables
Math 17
(UPIMath)
Systems
Lec 12
2 / 29
Aim for this Lecture
Previously: graphing lines, parabolas, circles
Math 17
(UPIMath)
Systems
Lec 12
3 / 29
Aim for this Lecture
Previously: graphing lines, parabolas, circles
Learn techniques in solving systems of equations
Math 17
(UPIMath)
Systems
Lec 12
3 / 29
Aim for this Lecture
Previously: graphing lines, parabolas, circles
Learn techniques in solving systems of equations
Solve algebraically for the intersections of graphs of equations
Math 17
(UPIMath)
Systems
Lec 12
3 / 29
Aim for this Lecture
Previously: graphing lines, parabolas, circles
Learn techniques in solving systems of equations
Solve algebraically for the intersections of graphs of equations
Graph equations with their intersections
Math 17
(UPIMath)
Systems
Lec 12
3 / 29
System of Equations
Definition
A
system of equations
is a set of two or more equations in several
equations.
A
solution
of a system is a solution common to all equations in the
system.
The
solution set
of a system is the set of all its solutions.
Math 17
(UPIMath)
Systems
Lec 12
4 / 29
Two Linear Equations in Two Variables
Definition
A
system of two linear equations in two variables
has the form
⇢
a
1
x
+
b
1
y
=
c
1
a
2
x
+
b
2
y
=
c
2
where
a
1
, a
2
, b
1
, b
2
, c
1
, c
2
2
.
Math 17
(UPIMath)
Systems
Lec 12
5 / 29
Graphical Interpretation of Linear Systems
Recall: A solution to an equation in two variables is a point on the graph of the
equation.
Math 17
(UPIMath)
Systems
Lec 12
6 / 29
Graphical Interpretation of Linear Systems
Recall: A solution to an equation in two variables is a point on the graph of the
equation.
For systems of two linear equations
in two variables, each equation
represents a line.
Math 17
(UPIMath)
Systems
Lec 12
6 / 29
Graphical Interpretation of Linear Systems
Recall: A solution to an equation in two variables is a point on the graph of the
equation.
For systems of two linear equations
in two variables, each equation
represents a line.
Example.
Solve the system
⇢
3
x

4
y
=
1
2
x
+ 3
y
=
12
Math 17
(UPIMath)
Systems
Lec 12
6 / 29
Graphical Interpretation of Linear Systems
Recall: A solution to an equation in two variables is a point on the graph of the
equation.
For systems of two linear equations
in two variables, each equation
represents a line.
)
A solution to the system is a
point on both lines.
Example.
Solve the system
⇢
3
x

4
y
=
1
2
x
+ 3
y
=
12
Math 17
(UPIMath)
Systems
Lec 12
6 / 29
Graphical Interpretation of Linear Systems
Recall: A solution to an equation in two variables is a point on the graph of the
equation.
You've reached the end of your free preview.
Want to read all 122 pages?
 Spring '11
 AaronJamesPorlante
 Math, Linear Equations, Systems Of Equations, Equations, Quadratic equation, Elementary algebra, Interpretation of Linear Systems