SOLUTION: Classify the following system of equations: -6x + 3y = 12 5y = 10x + 4 Consistent and independent Inconsistent Consistent and dependent

Algebra ->  Systems-of-equations -> SOLUTION: Classify the following system of equations: -6x + 3y = 12 5y = 10x + 4 Consistent and independent Inconsistent Consistent and dependent       Log On


   

Question 633830: Classify the following system of equations:
-6x + 3y = 12
5y = 10x + 4
Consistent and independent
Inconsistent
Consistent and dependent


Answer by MathLover1(20849) 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:


-6x%2B3y=12

-10x%2B5y=4





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%2B3y=12 Start with the given equation



3y=12%2B6x Add 6+x to both sides



3y=%2B6x%2B12 Rearrange the equation



y=%28%2B6x%2B12%29%2F%283%29 Divide both sides by 3



y=%28%2B6%2F3%29x%2B%2812%29%2F%283%29 Break up the fraction



y=2x%2B4 Reduce



Now lets graph y=2x%2B4 (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+2x%2B4%29+ Graph of y=2x%2B4




So let's solve for y on the second equation


-10x%2B5y=4 Start with the given equation



5y=4%2B10x Add 10+x to both sides



5y=%2B10x%2B4 Rearrange the equation



y=%28%2B10x%2B4%29%2F%285%29 Divide both sides by 5



y=%28%2B10%2F5%29x%2B%284%29%2F%285%29 Break up the fraction



y=2x%2B4%2F5 Reduce





Now lets add the graph of y=2x%2B4%2F5 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+2x%2B4%2C2x%2B4%2F5%29+ Graph of y=2x%2B4(red) and y=2x%2B4%2F5(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.