SOLUTION: Using the graphing method how many solutions does this system have. 6x-2y=4 12x-6y=8

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Question 126086This question is from textbook Algebra 1 Concepts and Skills
: Using the graphing method how many solutions does this system have. 6x-2y=4
12x-6y=8 This question is from textbook Algebra 1 Concepts and Skills

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:

6x-2y=4
12x-6y=8




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

6x-2y=4 Start with the given equation


-2y=4-6x Subtract 6+x from both sides


-2y=-6x%2B4 Rearrange the equation


y=%28-6x%2B4%29%2F%28-2%29 Divide both sides by -2


y=%28-6%2F-2%29x%2B%284%29%2F%28-2%29 Break up the fraction


y=3x-2 Reduce


Now lets graph y=3x-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+3x-2%29+ Graph of y=3x-2



So let's solve for y on the second equation

12x-6y=8 Start with the given equation


-6y=8-12x Subtract 12+x from both sides


-6y=-12x%2B8 Rearrange the equation


y=%28-12x%2B8%29%2F%28-6%29 Divide both sides by -6


y=%28-12%2F-6%29x%2B%288%29%2F%28-6%29 Break up the fraction


y=2x-4%2F3 Reduce



Now lets add the graph of y=2x-4%2F3 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x-2%2C2x-4%2F3%29+ Graph of y=3x-2(red) and y=2x-4%2F3(green)

From the graph, we can see that there is one solution (since one intersection corresponds to one solution)


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Answer:


So the system has one solution