SOLUTION: Determine if the system is Dependent, Inconsistent or has a Unique Solution. If it has a solution, find the solution for x and y using any method. 12x – 3y = 21 4x – y = 9

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Question 473087: Determine if the system is Dependent, Inconsistent or has a Unique Solution. If it has a solution, find the solution for x and y using any method.

12x – 3y = 21
4x – y = 9
Answer by MathLover1(20850)   (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:










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 parallel and will never intersect. So there are no solutions and the system is inconsistent.
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