SOLUTION: 5.6 Solve the system by the method of your choice x=6y+2 3x-18y=6 The solution set is { } (type and ordered pair)

Algebra ->  Graphs -> SOLUTION: 5.6 Solve the system by the method of your choice x=6y+2 3x-18y=6 The solution set is { } (type and ordered pair)      Log On


   

Question 1012161: 5.6
Solve the system by the method of your choice
x=6y+2
3x-18y=6
The solution set is { } (type and ordered pair)
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x=6y%2B2......eq.1
3x-18y=6......eq.2
---------------------
x-6y=2......eq.1
3x-18y=6......eq.2
---------------------

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x-6y=2

3x-18y=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-6y=2 Start with the given equation



-6y=2-x Subtract +x from both sides



-6y=-x%2B2 Rearrange the equation



y=%28-x%2B2%29%2F%28-6%29 Divide both sides by -6



y=%28-1%2F-6%29x%2B%282%29%2F%28-6%29 Break up the fraction



y=%281%2F6%29x-1%2F3 Reduce



Now lets graph y=%281%2F6%29x-1%2F3 (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%2F6%29x-1%2F3%29+ Graph of y=%281%2F6%29x-1%2F3




So let's solve for y on the second equation


3x-18y=6 Start with the given equation



-18y=6-3x Subtract 3+x from both sides



-18y=-3x%2B6 Rearrange the equation



y=%28-3x%2B6%29%2F%28-18%29 Divide both sides by -18



y=%28-3%2F-18%29x%2B%286%29%2F%28-18%29 Break up the fraction



y=%281%2F6%29x-1%2F3 Reduce





Now lets add the graph of y=%281%2F6%29x-1%2F3 to our first plot to get:


Graph of y=%281%2F6%29x-1%2F3(red) and y=%281%2F6%29x-1%2F3(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.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

5.6
Solve the system by the method of your choice
x=6y+2
3x-18y=6
The solution set is { } (type and ordered pair)
x = 6y + 2 ------- eq (i)

3x - 18y = 6_____3(x - 6y) = 3(2)_____x - 6y = 2_____x = 2 + 6y ------ eq (ii)

As seen, both equations are the same, so the system has an INFINITE NUMBER of solutions.