SOLUTION: Solve the system of equations by graphing. Then classify the systems as consistent or unconsistent and the equations as dependent or independent 3u+v=15 3u+v+33

Algebra ->  Linear-equations -> SOLUTION: Solve the system of equations by graphing. Then classify the systems as consistent or unconsistent and the equations as dependent or independent 3u+v=15 3u+v+33      Log On


   

Question 145809: Solve the system of equations by graphing. Then classify the systems as consistent or unconsistent and the equations as dependent or independent
3u+v=15
3u+v+33
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
note: I'm replacing "u" with "x" and "v" with "y"

Start with the given system of equations:

3x%2By=15
3x%2By=33




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

3x%2By=15 Start with the given equation


y=15-3x Subtract 3+x from both sides


y=-3x%2B15 Rearrange the equation


Now lets graph y=-3x%2B15 (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+-3x%2B15%29+ Graph of y=-3x%2B15



So let's solve for y on the second equation

3x%2By=33 Start with the given equation


y=33-3x Subtract 3+x from both sides


y=-3x%2B33 Rearrange the equation




Now lets add the graph of y=-3x%2B33 to our first plot to get:

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-3x%2B15%2C-3x%2B33%29+ Graph of y=-3x%2B15(red) and y=-3x%2B33(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.