ALGEBRA 2 LECTURE S – 1:
Solving Systems by Graphing or Substitution
Reading Assignment: Chapter 3, Pages 156 – 161
SYSTEMS OF EQUATIONS



A SYSTEM OF EQUATIONS is a collection of equations in the same variables.
The solution of a system of two linear equations in x and y is any ordered pair (x. y) that
satisfies both equations.
The solution (x, y) is also the point of intersection for the graphs of the lines in the
system.
CLASSIFYING SYSTEMS OF EQUATIONS
 If a system of equations has at least one solution, it is called CONSISTENT.
o If a system has exactly one solution it is called INDEPENDENT.
o If a system has infinitely many solutions, it is call DEPENDENT.
 If a system does not have a solution, it is called INCONSISTENT.
Classifying using Algebra
If solving using the addition
or substitution method leads to:
x = a number,
y = a number
then the system is:
and the equations:
INDEPENDENT
will have different values of m when
both are placed in y = mx + b
(slope-intercept) form
will have the same value of m, but
different values of b, when both are
placed in y = mx + b form
will be identical when both are placed
in slope-intercept form
an inconsistent equation,
such as 0 = 3
INCONSISTENT
An identity,
such as 5 = 5
DEPENDENT
Classifying by Graphing
If the equations have:
Different Slopes
Same Slope but Different
Intercepts
Same Slope and Same
Intercept
INDEPENDENT
y = x + 10
y = 2x
then the system is:
INDEPENDENT
INCONSISTENT
and the lines:
cross at a point
are parallel and never cross
DEPENDENT
are actually both the same line
INCONSISTENT
y=x
y = x + 10
DEPENDENT
y = x + 10
2y = 2x + 20
ALGEBRA 2 LECTURE S – 1:
Solving Systems by Graphing or Substitution
EXAMPLE 1:
Graph and classify each system. Then find the solution from the graph.
A. x + y = 5 and x – 5y = –7
B. x – 2y = 3 and x + 5 = 2y
TRY THIS Page 157:
Graph and classify: y = 3x + 4 and y = –2x + 4. Then find the solution from the graph.
EXAMPLE 2: Use substitution to solve the system: 2x + y = 3 and 3x – 2y = 8. Check your
solution.
TRY THIS Page 158:
Use substitution to solve the system: 3x + y = 8 and 18x + 2y = 4. Check your solution.
HW S – 1 Page 161 #17 – 31 ODDS