Solving Linear Systems
 Graphically
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Solve this system of equations graphically.

 4x - 6y = 12
2x + 2y = 6
 

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.
4x - 6y = 12
 4(3) - 6(0) = 12
12 - 0 = 12
12 = 12  (check)		 2x + 2y = 6
2(3) + 2(0) = 6
6 + 0 = 6
6 = 6 (check)
 

 

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.