3:1 Solving Systems of Equations by
Graphing
To solve systems of equations by graphing
 To determine whether a system of linear
equations is consistent and independent,
consistent and dependent or inconsistent

Warm-up: Type 1 writing
3 lines or more – 2 minutes
In purchasing a cell phone, you could either pay
$50/month + .02/text
or $40/month + .04/text.
How do you know which plan to choose?
30 seconds
Finish your thought.
System of equations:
A set of two or more equations that
contain the same variables
Example 1
Example 2
Example 3
Example 4
Example 5
Solve by Graphing
Break-Even Point Analysis
Intersecting Lines
Same Line
Parallel Lines
Solve the system of equations by graphing.
Write each equation in slope-intercept form.
The graphs appear to intersect
at (4, 2).
Check Substitute the coordinates into each equation.
Original equations
Replace x with
and y with 2.
Simplify.
Answer: The solution of the system is (4, 2).
4
Solve the system of equations by graphing.
Answer: (4, 1)
Break-even point:
In business applications, the point at
which the income equals the cost
Fund-raising A service club is selling copies of their holiday cookbook
to raise funds for a project. The printer’s set-up charge is $200, and each
book costs $2 to print. The cookbooks will sell for $6 each. How many
cookbooks must the members sell before they make a profit?
Let
Cost of books
y
is
=
cost per book
2x
plus
+
set-up charge.
200
Income from
books
y
is
price per
book
=
6
Answer:
The graphs intersect at (50,
300). This is the breakeven point. If the group sells
less than 50 books, they will
lose money. If the group
sells more than 50 books,
they will make a profit.
times
number of
books.
x
The student government is selling candy bars. It cost $1 for each candy
bar plus a $60 set-up fee. The group will sell the candy bars for $2.50
each. How many do they need to sell to break even?
Answer:
40 candy bars
Evaluate f(-4) for f(x) =│2x + 6│
1.
2.
3.
4.
5.
14
-2
4
12
2
Name that function
1.
2.
3.
4.
Step
Constant
Absolute Value
Round Down
Name that function
1.
2.
3.
4.
Step
Constant
Absolute Value
Piecewise
Consistent:
A system of equations that has at least
one solution
Inconsistent:
A system of equations that has no solution
(parallel lines)
Independent:
A system of equations that has exactly
one solution (intersecting lines)
Dependent:
A system of equations that has an infinite
number of solutions (same line)
Graph the system of equations and describe it as consistent and
independent, consistent and dependent, or inconsistent.
Write each equation in slope-intercept form.
Answer:
The graphs of the equations intersect at (2, –3). Since there is one solution
to this system, this system is consistent and independent.
Graph the system of equations and describe it as consistent and
independent, consistent and dependent, or inconsistent.
Answer:
consistent and
independent
Graph the system of equations and describe it as consistent and
independent, consistent and dependent, or inconsistent.
Since the equations are equivalent, their graphs
are the same line.
Answer:
Any ordered pair representing a point on that line will satisfy both equations.
So, there are infinitely many solutions. This system is consistent and
dependent.
Graph the system of equations and describe it as consistent and
independent, consistent and dependent, or inconsistent.
Answer:
consistent and
dependent
Graph the system of equations and describe it
as consistent and independent, consistent and dependent, or
inconsistent.
Answer:
The lines do not intersect. Their graphs are parallel lines. So, there
are no solutions that satisfy both equations. This system is
inconsistent.
Graph the system of equations and describe it
as consistent and independent, consistent and dependent, or
inconsistent.
Answer:
inconsistent