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

Algebra ->  Inequalities -> 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      Log On


   

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) About Me  (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:


12x-3y=21

4x-y=9





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


12x-3y=21 Start with the given equation



-3y=21-12x Subtract 12+x from both sides



-3y=-12x%2B21 Rearrange the equation



y=%28-12x%2B21%29%2F%28-3%29 Divide both sides by -3



y=%28-12%2F-3%29x%2B%2821%29%2F%28-3%29 Break up the fraction



y=4x-7 Reduce



Now lets graph y=4x-7 (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+4x-7%29+ Graph of y=4x-7




So let's solve for y on the second equation


4x-y=9 Start with the given equation



-y=9-4x Subtract 4+x from both sides



-y=-4x%2B9 Rearrange the equation



y=%28-4x%2B9%29%2F%28-1%29 Divide both sides by -1



y=%28-4%2F-1%29x%2B%289%29%2F%28-1%29 Break up the fraction



y=4x-9 Reduce





Now lets add the graph of y=4x-9 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4x-7%2C4x-9%29+ Graph of y=4x-7(red) and y=4x-9(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.