SOLUTION: Identify the solution(s) of the system of equations, if any. -4x - 6y = 12 12y = -8x - 24

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Question 951388: Identify the solution(s) of the system of equations, if any.
-4x - 6y = 12
12y = -8x - 24
Found 2 solutions by MathLover1, checkley77:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

-4x+-+6y+=+12....simplify, both sides divide by 2
12y+=+-8x+-+24.........both sides divide by 4
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-2x+-+3y+=+6
3y+=+-2x+-+6
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-2x+-+3y+=+6
2x%2B3y+=++-+6

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



Start with the given system of equations:


-2x-3y=6

2x%2B3y=-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


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



-3y=6%2B2x Add 2+x to both sides



-3y=%2B2x%2B6 Rearrange the equation



y=%28%2B2x%2B6%29%2F%28-3%29 Divide both sides by -3



y=%28%2B2%2F-3%29x%2B%286%29%2F%28-3%29 Break up the fraction



y=%28-2%2F3%29x-2 Reduce



Now lets graph y=%28-2%2F3%29x-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+%28-2%2F3%29x-2%29+ Graph of y=%28-2%2F3%29x-2




So let's solve for y on the second equation


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



3y=-6-2x Subtract 2+x from both sides



3y=-2x-6 Rearrange the equation



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



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



y=%28-2%2F3%29x-2 Reduce





Now lets add the graph of y=%28-2%2F3%29x-2 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%28-2%2F3%29x-2%2C%28-2%2F3%29x-2%29+ Graph of y=%28-2%2F3%29x-2(red) and y=%28-2%2F3%29x-2(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 checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
-4x - 6y = 12 add (+4x to both sides)
12y = -8x - 24
-6y = 4x + 12 multiply by 2 & add.
-12y=8x+24
12y=-8x-24 ADD
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0y=0x+0 indicates NO SOLUTION.