If you
can graph a straight line, you can solve systems of
equations graphically!
The
process is very easy.
Simply graph the two lines and look for the point where
they intersect (cross).
Systems of Equations may also be referred to as
"simultaneous equations".
Let's look at an example using a graphical method:
Solve graphically:
4x - 6y = 12
2x + 2y = 6
To solve a system of
equations graphically, graph both equations and see where
they intersect. The intersection point is the
solution.
First, solve each equation for "y =".
4x - 6y
= 12
slope
=
y-intercept = -2
2x + 2y = 6
slope = -1 y-intercept = 3
Graph the lines.
The slope intercept method of
graphing was used in this example.
The point of intersection of the
two lines, (3,0), is the solution to the system of equations.
This means that (3,0), when
substituted into either equation, will make them both true.
See the check.
Check:
Since the two lines cross at (3,0), the solution
is x = 3 and y = 0. Checking
these value shows that this answer is correct.
Plug these values into the ORIGINAL equations
and get a true result.
Grab you
Graphing Calculator: The graphing
calculator can solve systems of equations
graphically. Click the calculator at
the right for directions on using the
TI-83+/84+ graphing calculator to solve
systems of equations. Click calculator.