SOLUTION: Solve the following systems by graphing. How do I graph the equation? For example: 3x-6y= 9 x-2y= 3 Do I graph the these numbers from the equations 6y and 9, 2y and 3? Or do

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve the following systems by graphing. How do I graph the equation? For example: 3x-6y= 9 x-2y= 3 Do I graph the these numbers from the equations 6y and 9, 2y and 3? Or do      Log On


   

Question 118852: Solve the following systems by graphing.
How do I graph the equation? For example:
3x-6y= 9
x-2y= 3
Do I graph the these numbers from the equations 6y and 9, 2y and 3? Or do I work out the equations and graph the numbers from the answer to the equations?
Thank you for your assistance.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


3x-6y=9

1x-2y=3





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


3x-6y=9 Start with the given equation



-6y=9-3x Subtract 3+x from both sides



-6y=-3x%2B9 Rearrange the equation



y=%28-3x%2B9%29%2F%28-6%29 Divide both sides by -6



y=%28-3%2F-6%29x%2B%289%29%2F%28-6%29 Break up the fraction



y=%281%2F2%29x-3%2F2 Reduce



Now lets graph y=%281%2F2%29x-3%2F2 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F2%29x-3%2F2%29+ Graph of y=%281%2F2%29x-3%2F2




So let's solve for y on the second equation


1x-2y=3 Start with the given equation



-2y=3-x Subtract +x from both sides



-2y=-x%2B3 Rearrange the equation



y=%28-x%2B3%29%2F%28-2%29 Divide both sides by -2



y=%28-1%2F-2%29x%2B%283%29%2F%28-2%29 Break up the fraction



y=%281%2F2%29x-3%2F2 Reduce





Now lets add the graph of y=%281%2F2%29x-3%2F2 to our first plot to get:


Graph of y=%281%2F2%29x-3%2F2(red) and y=%281%2F2%29x-3%2F2(green)


From the graph, we can see that the two lines are identical (one lies perfectly on top of the other) and intersect at all points of both lines. So there are an infinite number of solutions and the system is dependent.