Example ONE:
Solve the Linear System by Graphing.

Equation one: 4x - 6y = 2
Equation two: 2x + 2y = 6

Begin by graphing both equations as shown at the right. From the graph you interpret that the line intersects at (2,1). You can check the solution as follows:

Equation one: 4(2) - 6 (1) = 2
Equation two: 2(2) + 2(1) = 6

The solution of this system of linear equations is (2,1).

Example TWO:
Solve the word problem by graphing.

You are trying to decorate your new Chevy Silverado. You want to buy both the Chevy bowtie emblems and bumper stickers. The bowtie emblems cost $.10 each and the bumper stickers cost $.50 each. You need 125 decorations in all and you have $32.50 to spend. How many of each can you buy?

x = bowtie emblems
y = bumper stickers

x + y = 125
0.1x + 0.5y = 32.5

Now once you have the equations you must graph them.

From the graph you interpret that the line intersects at (75,50). You can check if this solution is correct by putting the solution back into the equations.

You find that the solution is correct. Therefore you can purchase 75 bowtie emblems and 50 bumper stickers.

 

 

 

\

Systems with Many or No Solutions

Graphical Interpretation	Algebraic Interpretation
The graph of the system is a pair of lines that intersect at one point.	The system has exactly one solution.
The graph of the system is a single line.	The system has infinitely many solutions.
The graph of the system is a pair of parallel lines so that there is no point of intersection.	The system has no solutions.