SOLUTION: Solve the system by graphing. x - y = 2 3x - 3y = 6 Thanks for your help, I've been stuck on this one for a while.

Algebra ->  Coordinate-system -> SOLUTION: Solve the system by graphing. x - y = 2 3x - 3y = 6 Thanks for your help, I've been stuck on this one for a while.      Log On


   

Question 116852: Solve the system by graphing.
x - y = 2
3x - 3y = 6
Thanks for your help, I've been stuck on this one for a while.
Answer by MathLover1(20849) 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:


1x-y=2

3x-3y=6





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


1x-y=2 Start with the given equation



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



-y=-x%2B2 Rearrange the equation



y=%28-x%2B2%29%2F%28-1%29 Divide both sides by -1



y=%28-1%2F-1%29x%2B%282%29%2F%28-1%29 Break up the fraction



y=x-2 Reduce



Now lets graph y=x-2 (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+x-2%29+ Graph of y=x-2




So let's solve for y on the second equation


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



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



-3y=-3x%2B6 Rearrange the equation



y=%28-3x%2B6%29%2F%28-3%29 Divide both sides by -3



y=%28-3%2F-3%29x%2B%286%29%2F%28-3%29 Break up the fraction



y=x-2 Reduce





Now lets add the graph of y=x-2 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-2%2Cx-2%29+ Graph of y=x-2(red) and y=x-2(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.