7-1 Graphing Systems of
Equations
SWBAT:
1) Solve systems of linear equations by graphing
2) Determine whether a system of linear equations is consistent and
independent, consistent and dependent, or inconsistent
What is a System of Equations?
• A system of equations is two or more equations with the
same variables
• The solution to a system of equations is the ordered pair
that is a common solution of all the equations
• One way we can solve a system of equations is by graphing
the equations on the same coordinate plane
Lets Look at our Packet…
They intersect at (2,4),
and both have it as a
solution.
Look at another…
So they both have (1,4) as a solution.
One more!
y = 4/3 x - 4
y = 2/3 x - 6
So they both have (-3,8) as a solution.
Consistent and Independent
• When two lines intersect, a system of
equations has one solution (meaning only
one point will satisfy the system).
• When a system has one solution, the system
is said to be consistent and independent.
Wait…What About?
These two lines are
parallel! They have
same exact slope
They will never cross!
Inconsistent
• This would occur if the equations
never intersect (they are parallel).
They have no common coordinates.
• When a system of equations has no
solution, the system is said to be
inconsistent.
What happens here?
y = -5x - 2
These two lines the same
equation!
They are the same exact line!
Consistent and Dependent
• This would occur if the equations are
the same exact line.
• All the coordinates are the exact
same. So there are infinite solutions.
• When a system of equations has
infinitely many solutions, the system
is said to be consistent and dependent.
Summary…
Example 2: Solve the system of equations by graphing. Then
describe the solution.
b)
c)
y = 4- x
x=2