SOLUTION: Determine whether the pair of lines is parallel, perpendicular, or neither 2x+y=5 , 6×+3y=4

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Question 759929: Determine whether the pair of lines is parallel, perpendicular, or neither 2x+y=5 , 6×+3y=4
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Determine whether the pair of lines is parallel, perpendicular, or neither 2x+y=5 , 6×+3y=4
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y = -2x + 5
y = -2x + 3/4
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slopes are the same so the lines are parallel.
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Cheers,
Stan H.
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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+2x%2By=5
+6x%2B3y=4

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



Start with the given system of equations:


2x%2By=5

6x%2B3y=4





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


2x%2By=5 Start with the given equation



1y=5-2x Subtract 2+x from both sides



1y=-2x%2B5 Rearrange the equation



y=%28-2x%2B5%29%2F%281%29 Divide both sides by 1



y=%28-2%2F1%29x%2B%285%29%2F%281%29 Break up the fraction



y=-2x%2B5 Reduce



Now lets graph y=-2x%2B5 (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+-2x%2B5%29+ Graph of y=-2x%2B5




So let's solve for y on the second equation


6x%2B3y=4 Start with the given equation



3y=4-6x Subtract 6+x from both sides



3y=-6x%2B4 Rearrange the equation



y=%28-6x%2B4%29%2F%283%29 Divide both sides by 3



y=%28-6%2F3%29x%2B%284%29%2F%283%29 Break up the fraction



y=-2x%2B4%2F3 Reduce





Now lets add the graph of y=-2x%2B4%2F3 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-2x%2B5%2C-2x%2B4%2F3%29+ Graph of y=-2x%2B5(red) and y=-2x%2B4%2F3(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.