Question 129071: hello i am trying to understand and figure out how to solve graphing.. example.
3x - 6y = 12
2x - 4y = 8 can you please help me .. i am lost don't know how or where to begin very confused ... I hope to here from you thank you for your time... i really wanna know and understand how to figure problems like this out and then solve each problem out by graphing. also I am asked to write no solution or infinitely many. please help... sorry but my problem is not from a text book it is from a mixed exercise sheet practice 6-1 solving systems by graphing algebra .
thanks: Robert Tisdale
8th grade math
but I am in 9th grade and still cant understand
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Ok, the idea behind solving systems of linear equations by graphing is to get a picture (called a graph) of the lines represented by the equations.
Once you have the graph, you can see if the lines cross, or if they are parallel, or if they are one-and-the-same line.
If the lines cross, the the solution is the point of intersection of the lines.
If the lines are parallel, then there is no solution because there is no intersection.
Finally, if the lines are one-and-the-same, that is they are the same line, then there are infinitely many solutions because every point on one of the lines also lies on the other line.
To graph the lines from the given equations, first change the equations into their slope-intercept form: y = mx+b
 changes to: 
 changes to:
As you can see, these two equations are identical and you would expect them to produce exactly the same line when graphed.
To graph these, you will need to select a value for x, substitute it into the equation, and solve for the corresponding value of y. This will get you one point that you can place on your coordinate graph paper.
Select a different value for x and find its corresponding value of y.
This will get you a second point to put on your graph. Now you join these two points with a straight line and you will have graphed the equation.
To make the calculations easy, choose x = 0 and x = 4.
For x = 0:
 so for the first point, you have (0, -2) and...
For x = 4:
 so for the second point, you have (4, 0)
The two equations produce exactly the same line, this being the case, the solution is "infinitely many"
Let's see what the graphs look like, and I'll put each line on a separate graph.
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