Math A

Solving Systems of Equations Graphically 

 

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).

 

Solving Systems of Equations by Graphing

To solve a system of equations graphically, graph both equations and see where they intersect.  The intersection point is the solution.

Solve Graphically

4x-6y=12
2x+2y=6

 


Solve each equation for "y=".

 

4x-6y=12
4x=6y+12
4x-12=6y
6y=4x-12
y=(4/6)x-(12/6)
y=(2/3)x-2

slope = 2/3
y-intercept = -2

2x+2y=6
2y=-2x+6
y=(-2/2)x+(6/2)
y=-x+3

slope=-1/1
y-intercept = 3

 

 

Graph the equations.

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.

 

How to use your
TI-83+ graphing calculator  with systems of equations.
Click calculator.

 

 

 

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Roberts