SOLUTION: Solve the following system of equations by graphing. If the system is inconsistent or the equations are​ dependent, say so. 24x-4y=48 6x=y+12

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Question 1089059: Solve the following system of equations by graphing. If the system is inconsistent or the equations are​ dependent, say so.
24x-4y=48
6x=y+12
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
4y=24x-48, after rearranging, and that is y=6x-12
y=6x-12
These are dependent equations; they are the same line.
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!



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



Start with the given system of equations:










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


Start with the given equation



Subtract from both sides



Rearrange the equation



Divide both sides by



Break up the fraction



Reduce



Now lets graph (note: if you need help with graphing, check out this solver)



Graph of




So let's solve for y on the second equation


Start with the given equation



Subtract from both sides



Rearrange the equation



Divide both sides by



Break up the fraction



Reduce





Now lets add the graph of to our first plot to get:


Graph of (red) and (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.
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