SOLUTION: Solve the system by graphing. x + 2y = 4 x + 2y = –2

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Question 113305: Solve the system by graphing.
x + 2y = 4
x + 2y = –2
Answer by MathLover1(20850) 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%2B2y=4

1x%2B2y=-2





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%2B2y=4 Start with the given equation



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



2y=-x%2B4 Rearrange the equation



y=%28-x%2B4%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%284%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x%2B2 Reduce



Now lets graph y=%28-1%2F2%29x%2B2 (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+%28-1%2F2%29x%2B2%29+ Graph of y=%28-1%2F2%29x%2B2




So let's solve for y on the second equation


1x%2B2y=-2 Start with the given equation



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



2y=-x-2 Rearrange the equation



y=%28-x-2%29%2F%282%29 Divide both sides by 2



y=%28-1%2F2%29x%2B%28-2%29%2F%282%29 Break up the fraction



y=%28-1%2F2%29x-1 Reduce





Now lets add the graph of y=%28-1%2F2%29x-1 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F2%29x%2B2%2C%28-1%2F2%29x-1%29+ Graph of y=%28-1%2F2%29x%2B2(red) and y=%28-1%2F2%29x-1(green)


From the graph, we can see that the two lines are parallel and will never intersect. So there are no solutions and the system is inconsistent.