SOLUTION: Identify the solution(s) of the system of equations, if any. -3x-4y=2 8y=-6x-4

Algebra ->  Graphs -> SOLUTION: Identify the solution(s) of the system of equations, if any. -3x-4y=2 8y=-6x-4       Log On


   

Question 973058: Identify the solution(s) of the system of equations, if any.
-3x-4y=2
8y=-6x-4
















































































Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

-3x-4y=2....eq.1.....both sides multiply by 2
8y=-6x-4+....eq.2....write in standard form
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-6x-8y=2....eq.1
6x%2B8y=-4+....eq.2
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Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


-6x-8y=4

6x%2B8y=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


-6x-8y=4 Start with the given equation



-8y=4%2B6x Add 6+x to both sides



-8y=%2B6x%2B4 Rearrange the equation



y=%28%2B6x%2B4%29%2F%28-8%29 Divide both sides by -8



y=%28%2B6%2F-8%29x%2B%284%29%2F%28-8%29 Break up the fraction



y=%28-3%2F4%29x-1%2F2 Reduce



Now lets graph y=%28-3%2F4%29x-1%2F2 (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+%28-3%2F4%29x-1%2F2%29+ Graph of y=%28-3%2F4%29x-1%2F2




So let's solve for y on the second equation


6x%2B8y=2 Start with the given equation



8y=2-6x Subtract 6+x from both sides



8y=-6x%2B2 Rearrange the equation



y=%28-6x%2B2%29%2F%288%29 Divide both sides by 8



y=%28-6%2F8%29x%2B%282%29%2F%288%29 Break up the fraction



y=%28-3%2F4%29x%2B1%2F4 Reduce





Now lets add the graph of y=%28-3%2F4%29x%2B1%2F4 to our first plot to get:


Graph of y=%28-3%2F4%29x-1%2F2(red) and y=%28-3%2F4%29x%2B1%2F4(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.