Download Solving Systems of Equations by Graphing

Solving Linear
Systems
Graphing
3-1 Graphing Systems of
Equations
A system is a group of two
or more equations.
The SOLUTION to the
system is the point that solves
ALL the equations.
Systems of Equations
What do solutions to linear
equations look like?
Ordered pairs
The solution to the system
will be an ordered pair.
Systems of Equations
Points make up lines, the
solutions to the equations are
the points that make up the
lines.
Thus the point that is the
solution will be on both lines.
Systems of Equations
There are several ways to
solve systems: algebraically,
graphically, and by
substitution.
We will only be using
graphing.
Solving Systems of Equations
If the lines cross once, there
will be one solution.
If the lines are parallel,
there will be no solutions.
If the lines are the same,
there will be an infinite
number of solutions.
Solving systems of Equations
Refer to worksheet 3-1 for
examples. (PWS 3-1 on
ibooks)
Find the solution to the
following system:
2x + y = 4
x-y=2
Solving Systems of Equations
1) solve each equation for y
and graph them.
y = -2x + 4 & y = x - 2
2) find the point where the
graphs intersect.
y = -2x + 4 & y = x - 2
x
y
Solving Systems of Equations
The two lines cross at the
point (2, 0). So the solution
to the system is (2, 0).
To check your solution, plug
it into each equation and see
if you get a true statement.
Solving Systems of Equations
Continue with PWS 3-1 as
practice/examples.
Solving systems using the
calculators
Go to the graph menu (5)
Type in your first equation
for y1 and your second in y2.
Hit F6 to graph.
Determine point of
intersection: Shift, F5, F5